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Find the value of $1-2+3-4+\cdots+2015-2016+2017$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2016+2017) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1\\ -4+5 &= 5-4 = 1\\ & \hspace{2.5mm} \vdots \\ \ -2016 &+ 2017 = 1 \end{align*} \begin{equation*} (2016\div 2)\times 1 + 1 = 1009 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2016+2017) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1\\ -4+5 &= 5-4 = 1\\ & \hspace{2.5mm} \vdots \\ \ -2016 &+ 2017 = 1 \end{align*} \begin{equation*} (2016\div 2)\times 1 + 1 = 1009 \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2017}\right)\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2016}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2017}\right)\left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2016}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2007}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2016}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2017} \end{equation*}
Given that $$S=\dfrac{1}{\frac{1}{2008}+\frac{1}{2009}+\frac{1}{2010}+\cdots+\frac{1}{2017}}.$$ Find the largest whole number smaller than $S$.
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Assume all to be $\frac{1}{2008}$ \begin{equation} \frac{1}{\frac{10}{2008}} = 200.8 \end{equation} assume all to be $\frac{1}{2017}$ \begin{equation} \frac{1}{\frac{10}{2017}}=201.7 \end{equation} \begin{equation} 200.8 < S < 201.7 \end{equation} $c=7$.
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Assume all to be $\frac{1}{2008}$ \begin{equation} \frac{1}{\frac{10}{2008}} = 200.8 \end{equation} assume all to be $\frac{1}{2017}$ \begin{equation} \frac{1}{\frac{10}{2017}}=201.7 \end{equation} \begin{equation} 200.8 < S < 201.7 \end{equation} $c=7$.
Find the value of $1-2+3-4+\cdots+1907-1908+1909$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1908+1909) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1908 &+ 1909 = 1 \end{align*} \begin{equation*} (1908\div 2)\times 1 + 1 = 955 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1908+1909) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1908 &+ 1909 = 1 \end{align*} \begin{equation*} (1908\div 2)\times 1 + 1 = 955 \end{equation*}
Find the value of $1-2+3-4+\cdots+1915-1916+1917$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1916+1917) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1916 &+ 1917 = 1 \end{align*} \begin{equation*} (1916\div 2)\times 1 + 1 = 959 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1916+1917) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1916 &+ 1917 = 1 \end{align*} \begin{equation*} (1916\div 2)\times 1 + 1 = 959 \end{equation*}
Find the value of $1-2+3-4+\cdots+1917-1918+1919$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1918+1919) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1918 &+ 1919 = 1 \end{align*} \begin{equation*} (1918\div 2)\times 1 + 1 = 960 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1918+1919) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1918 &+ 1919 = 1 \end{align*} \begin{equation*} (1918\div 2)\times 1 + 1 = 960 \end{equation*}
Find the value of $1-2+3-4+\cdots+1937-1938+1939$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1938+1939) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1938 &+ 1939 = 1 \end{align*} \begin{equation*} (1938\div 2)\times 1 + 1 = 970 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1938+1939) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1938 &+ 1939 = 1 \end{align*} \begin{equation*} (1938\div 2)\times 1 + 1 = 970 \end{equation*}
Find the value of $1-2+3-4+\cdots+1957-1958+1959$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1958+1959) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1958 &+ 1959 = 1 \end{align*} \begin{equation*} (1958\div 2)\times 1 + 1 = 980 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1958+1959) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1958 &+ 1959 = 1 \end{align*} \begin{equation*} (1958\div 2)\times 1 + 1 = 980 \end{equation*}
Find the value of $1-2+3-4+\cdots+1997-1998+1999$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1998+1999) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1998 &+ 1999 = 1 \end{align*} \begin{equation*} (1998\div 2)\times 1 + 1 = 1000 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1998+1999) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1998 &+ 1999 = 1 \end{align*} \begin{equation*} (1998\div 2)\times 1 + 1 = 1000 \end{equation*}
Find the value of $1-2+3-4+\cdots+2019-2020+2021$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2020+2021) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2020 &+ 2021 = 1 \end{align*} \begin{equation*} (2020\div 2)\times 1 + 1 = 1011 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2020+2021) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2020 &+ 2021 = 1 \end{align*} \begin{equation*} (2020\div 2)\times 1 + 1 = 1011 \end{equation*}
Find the value of $1-2+3-4+\cdots+2039-2040+2041$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2040+2041) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2040 &+ 2041 = 1 \end{align*} \begin{equation*} (2040\div 2)\times 1 + 1 = 1021 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2040+2041) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2040 &+ 2041 = 1 \end{align*} \begin{equation*} (2040\div 2)\times 1 + 1 = 1021 \end{equation*}
Find the value of $1-2+3-4+\cdots+2075-2076+2077$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2076+2077) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2076 &+ 2077 = 1 \end{align*} \begin{equation*} (2076\div 2)\times 1 + 1 = 1039 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2076+2077) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2076 &+ 2077 = 1 \end{align*} \begin{equation*} (2076\div 2)\times 1 + 1 = 1039 \end{equation*}
Find the value of $1-2+3-4+\cdots+2097-2098+2099$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2098+2099) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2098 &+ 2099 = 1 \end{align*} \begin{equation*} (2098\div 2)\times 1 + 1 = 1050 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2098+2099) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2098 &+ 2099 = 1 \end{align*} \begin{equation*} (2098\div 2)\times 1 + 1 = 1050 \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2251}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2250}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2251}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2250}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2251}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2250}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2251} \end{equation*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2251}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2250}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2251} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1645}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1644}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1645}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1644}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1645}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1644}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1645} \end{equation*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1645}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1644}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1645} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1978}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1977}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1978}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1977}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1978}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1977}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1978} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1978}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1977}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1978} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2204}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2203}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2204}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2203}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2204}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2203}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2204} \end{equation*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2204}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2203}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2204} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2027}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2026}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2027}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2026}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2027}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2026}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2027} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2027}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2026}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2027} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1874}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1873}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1874}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1873}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1874}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1873}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1874} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1874}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1873}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1874} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2139}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2138}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2139}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2138}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2139}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2138}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2139} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2139}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2138}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2139} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1694}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1693}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1694}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1693}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1694}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1693}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1694} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1694}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1693}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1694} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1976}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1975}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1976}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1975}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1976}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1975}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1976} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1976}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1975}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1976} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1611}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1610}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1611}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1610}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1611}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1610}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1611} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1611}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1610}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1611} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2062}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2061}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2062}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2061}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2062}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2061}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2062} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2062}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2061}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2062} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1612}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1611}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1612}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1611}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1612}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1611}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1612} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1612}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1611}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1612} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1779}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1778}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1779}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1778}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1779}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1778}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1779} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1779}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1778}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1779} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1988}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1987}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1988}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1987}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1988}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1987}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1988} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1988}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1987}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1988} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1984}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1983}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1984}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1983}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1984}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1983}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1984} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1984}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1983}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1984} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2290}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2289}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2290}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2289}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2290}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2289}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2290} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2290}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2289}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2290} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1589}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1588}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1589}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1588}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1589}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1588}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1589} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1589}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1588}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1589} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2167}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2166}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2167}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2166}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2167}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2166}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2167} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2167}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2166}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2167} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1666}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1665}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1666}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1665}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1666}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1665}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1666} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1666}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1665}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1666} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2352}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2351}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2352}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2351}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2352}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2351}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2352} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2352}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2351}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2352} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1990}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1989}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1990}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1989}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1990}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1989}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1990} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1990}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1989}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1990} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1722}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1721}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1722}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1721}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1722}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1721}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1722} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1722}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1721}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1722} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2012}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2011}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2012}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2011}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2012}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2011}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2012} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2012}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2011}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2012} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1643}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1642}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1643}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1642}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1643}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1642}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1643} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1643}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1642}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1643} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2116}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2115}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2116}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2115}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2116}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2115}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2116} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2116}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2115}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2116} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1688}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1687}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1688}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1687}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1688}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1687}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1688} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1688}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1687}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1688} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1629}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1628}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1629}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1628}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1629}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1628}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1629} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1629}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1628}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1629} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1527}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1526}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1527}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1526}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1527}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1526}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1527} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1527}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1526}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1527} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2032}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2031}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2032}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2031}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2032}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2031}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2032} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2032}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2031}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2032} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1603}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1602}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1603}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1602}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1603}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1602}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1603} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1603}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1602}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1603} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1606}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1605}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1606}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1605}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1606}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1605}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1606} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1606}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1605}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1606} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2114}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2113}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2114}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2113}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2114}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2113}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2114} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2114}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2113}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2114} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1902}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1901}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1902}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1901}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1902}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1901}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1902} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1902}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1901}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1902} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2298}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2297}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2298}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2297}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2298}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2297}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2298} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2298}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2297}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2298} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2261}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2260}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2261}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2260}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2261}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2260}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2261} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2261}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2260}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2261} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1641}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1640}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1641}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1640}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1641}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1640}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1641} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1641}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1640}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1641} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2157}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2156}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2157}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2156}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2157}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2156}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2157} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2157}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2156}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2157} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2368}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2367}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2368}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2367}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2368}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2367}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2368} \end{equation*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2368}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2367}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2368} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2438}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2437}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2438}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2437}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2438}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2437}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2438} \end{equation*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2438}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2437}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2438} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2388}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2387}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2388}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2387}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2388}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2387}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2388} \end{equation*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2388}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2387}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2388} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2193}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2192}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2193}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2192}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2193}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2192}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2193} \end{equation*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2193}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2192}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2193} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1734}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1733}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1734}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1733}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1734}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1733}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1734} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1734}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1733}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1734} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2022}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2021}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2022}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2021}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2022}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2021}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2022} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2022}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2021}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2022} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1806}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1805}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1806}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1805}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1806}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1805}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1806} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1806}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1805}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1806} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1812}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1811}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1812}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1811}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1812}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1811}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1812} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1812}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1811}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1812} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2430}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2429}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2430}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2429}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2430}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2429}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2430} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2430}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2429}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2430} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2396}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2395}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2396}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2395}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2396}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2395}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2396} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2396}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2395}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2396} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1994}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1993}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1994}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1993}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1994}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1993}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1994} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1994}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1993}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1994} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1530}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1529}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1530}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1529}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1530}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1529}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1530} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1530}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1529}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1530} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1534}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1533}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1534}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1533}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1534}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1533}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1534} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1534}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1533}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1534} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2478}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2477}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2478}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2477}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2478}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2477}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2478} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2478}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2477}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2478} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1909}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1908}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1909}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1908}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1909}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1908}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1909} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1909}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1908}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1909} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2454}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2453}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2454}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2453}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2454}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2453}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2454} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2454}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2453}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2454} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1599}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1598}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1599}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1598}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1599}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1598}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1599} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1599}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1598}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1599} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2013}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2012}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2013}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2012}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2013}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2012}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2013} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2013}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2012}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2013} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1510}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1509}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1510}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1509}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1510}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1509}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1510} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1510}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1509}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1510} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2232}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2231}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2232}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2231}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2232}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2231}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2232} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2232}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2231}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2232} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2151}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2150}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2151}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2150}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2151}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2150}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2151} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2151}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2150}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2151} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2023}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2022}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2023}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2022}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2023}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2022}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2023} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2023}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2022}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2023} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2059}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2058}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2059}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2058}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2059}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2058}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2059} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2059}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2058}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2059} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2257}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2256}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2257}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2256}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2257}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2256}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2257} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2257}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2256}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2257} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2351}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2350}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2351}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2350}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2351}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2350}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2351} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2351}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2350}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2351} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1549}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1548}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1549}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1548}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1549}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1548}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1549} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1549}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1548}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1549} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1928}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1927}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1928}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1927}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1928}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1927}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1928} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1928}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1927}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1928} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1841}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1840}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1841}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1840}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1841}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1840}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1841} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1841}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1840}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1841} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1833}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1832}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1833}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1832}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1833}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1832}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1833} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1833}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1832}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1833} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2300}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2299}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2300}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2299}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2300}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2299}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2300} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2300}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2299}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2300} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1720}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1719}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1720}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1719}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1720}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1719}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1720} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1720}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1719}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1720} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2120}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2119}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2120}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2119}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2120}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2119}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2120} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2120}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2119}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2120} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2399}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2398}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2399}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2398}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2399}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2398}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2399} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2399}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2398}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2399} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1685}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1684}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1685}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1684}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1685}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1684}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1685} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1685}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1684}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1685} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2390}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2389}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2390}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2389}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2390}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2389}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2390} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2390}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2389}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2390} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1538}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1537}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1538}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1537}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1538}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1537}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1538} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1538}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1537}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1538} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1888}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1887}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1888}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1887}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1888}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1887}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1888} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1888}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1887}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1888} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1512}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1511}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1512}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1511}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1512}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1511}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1512} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1512}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1511}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1512} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2408}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2407}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2408}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2407}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2408}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2407}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2408} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2408}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2407}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2408} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2288}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2287}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2288}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2287}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2288}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2287}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2288} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2288}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2287}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2288} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1824}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1823}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1824}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1823}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1824}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1823}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1824} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1824}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1823}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1824} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1713}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1712}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1713}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1712}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1713}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1712}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1713} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1713}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1712}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1713} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2452}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2451}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2452}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2451}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2452}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2451}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2452} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2452}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2451}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2452} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2104}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2103}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2104}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2103}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2104}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2103}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2104} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2104}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2103}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2104} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2064}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2063}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2064}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2063}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2064}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2063}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2064} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2064}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2063}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2064} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1838}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1837}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1838}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1837}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1838}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1837}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1838} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1838}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1837}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1838} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2244}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2243}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2244}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2243}\right) \end{align*}
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\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2244}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2243}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2244} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2244}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2243}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2244} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1896}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1895}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1896}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1895}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1896}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1895}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1896} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1896}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1895}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1896} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2277}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2276}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2277}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2276}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2277}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2276}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2277} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2277}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2276}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2277} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2303}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2302}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2303}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2302}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2303}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2302}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2303} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2303}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2302}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2303} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1665}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1664}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1665}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1664}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1665}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1664}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1665} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1665}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1664}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1665} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1802}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1801}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1802}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1801}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1802}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1801}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1802} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1802}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1801}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{1802} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2359}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2358}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{2359}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2358}\right) \end{align*}
Sorry. Please check the correct answer below.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2359}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2358}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2359} \end{equation*}
Yay! Your are right.
\begin{align*} \text{Let } A&= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2359}\right) \\ B &= \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{2358}\right) \end{align*} \begin{equation*} A\times (1+B)-(1+A)\times B = \tfrac{1}{2359} \end{equation*}
Evaluate \begin{align*} \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1869}\right) \left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1868}\right) \\ -\left(1+\tfrac{1}{2}+\cdots+\tfrac{1}{1869}\right) \left(\tfrac{1}{2}+\tfrac{1}{3}+\cdots+\tfrac{1}{1868}\right) \end{align*}