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Permutation and Combination
Question 1 of 100
Melvin used the numbers 1, 2, 3, 4, 5, 6 and 7, without repeat, to form three 2-digit numbers and one 1-digit number. The sum of the four numbers is 100. Find the largest 2-digit number Melvin formed.
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Let the 4 numbers be $\overline{ab}$, $\overline{cd}$, $\overline{ef}$, $g$ we have $10(a+c+e)+(b+d+f+g)=100$ we know that $(b+d+f+g)$ must be a multiple of 10, either 10 or 20 since $1+2+3+\cdots+7 =28$. $\therefore\ (a+c+e)=28-10=18$ $\begin{aligned} &\text{When } (b+d+f+g) = 10, \\ & 10(a+c+e)+(b+d+f+g)=190 \text{ (reject)} \\ & \text{when } (b+d+f+g) = 20 \\ & (a+c+e) = 8 \\ & 10(a+c+e)+(b+d+f+g)=100 \text{ (accept)} \\ & \text{Try: } b,\, d,\, f,\, g \to 3,\, 4,\,6,\,7 \\ & a,\, c,\, e \to 1,\, 2,\, 5 \\ & \therefore\ \overline{ef} \to 57 \end{aligned}$
Yay! Your are right.
Let the 4 numbers be $\overline{ab}$, $\overline{cd}$, $\overline{ef}$, $g$ we have $10(a+c+e)+(b+d+f+g)=100$ we know that $(b+d+f+g)$ must be a multiple of 10, either 10 or 20 since $1+2+3+\cdots+7 =28$. $\therefore\ (a+c+e)=28-10=18$ $\begin{aligned} &\text{When } (b+d+f+g) = 10, \\ & 10(a+c+e)+(b+d+f+g)=190 \text{ (reject)} \\ & \text{when } (b+d+f+g) = 20 \\ & (a+c+e) = 8 \\ & 10(a+c+e)+(b+d+f+g)=100 \text{ (accept)} \\ & \text{Try: } b,\, d,\, f,\, g \to 3,\, 4,\,6,\,7 \\ & a,\, c,\, e \to 1,\, 2,\, 5 \\ & \therefore\ \overline{ef} \to 57 \end{aligned}$
Find the value of $1-2+3-4+\cdots+1899-1900+1901$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1900+1901) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1900 &+ 1901 = 1 \end{align*} \begin{equation*} (1900\div 2)\times 1 + 1 = 951 \end{equation*}
Find the value of $1-2+3-4+\cdots+1901-1902+1903$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1902+1903) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1902 &+ 1903 = 1 \end{align*} \begin{equation*} (1902\div 2)\times 1 + 1 = 952 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1902+1903) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1902 &+ 1903 = 1 \end{align*} \begin{equation*} (1902\div 2)\times 1 + 1 = 952 \end{equation*}
Find the value of $1-2+3-4+\cdots+1903-1904+1905$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1904+1905) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1904 &+ 1905 = 1 \end{align*} \begin{equation*} (1904\div 2)\times 1 + 1 = 953 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1904+1905) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1904 &+ 1905 = 1 \end{align*} \begin{equation*} (1904\div 2)\times 1 + 1 = 953 \end{equation*}
Find the value of $1-2+3-4+\cdots+1905-1906+1907$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1906+1907) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1906 &+ 1907 = 1 \end{align*} \begin{equation*} (1906\div 2)\times 1 + 1 = 954 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1906+1907) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1906 &+ 1907 = 1 \end{align*} \begin{equation*} (1906\div 2)\times 1 + 1 = 954 \end{equation*}
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 $1-2+3-4+\cdots+1909-1910+1911$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1910+1911) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1910 &+ 1911 = 1 \end{align*} \begin{equation*} (1910\div 2)\times 1 + 1 = 956 \end{equation*}
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1910+1911) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1910 &+ 1911 = 1 \end{align*} \begin{equation*} (1910\div 2)\times 1 + 1 = 956 \end{equation*}
Find the value of $1-2+3-4+\cdots+1911-1912+1913$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1912+1913) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1912 &+ 1913 = 1 \end{align*} \begin{equation*} (1912\div 2)\times 1 + 1 = 957 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1912+1913) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1912 &+ 1913 = 1 \end{align*} \begin{equation*} (1912\div 2)\times 1 + 1 = 957 \end{equation*}
Find the value of $1-2+3-4+\cdots+1913-1914+1915$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1914+1915) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1914 &+ 1915 = 1 \end{align*} \begin{equation*} (1914\div 2)\times 1 + 1 = 958 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1914+1915) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1914 &+ 1915 = 1 \end{align*} \begin{equation*} (1914\div 2)\times 1 + 1 = 958 \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*}
Yay! Your are right.
\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*}
Yay! Your are right.
\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 $1-2+3-4+\cdots+1919-1920+1921$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1920+1921) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1920 &+ 1921 = 1 \end{align*} \begin{equation*} (1920\div 2)\times 1 + 1 = 961 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1920+1921) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1920 &+ 1921 = 1 \end{align*} \begin{equation*} (1920\div 2)\times 1 + 1 = 961 \end{equation*}
Find the value of $1-2+3-4+\cdots+1921-1922+1923$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1922+1923) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1922 &+ 1923 = 1 \end{align*} \begin{equation*} (1922\div 2)\times 1 + 1 = 962 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1922+1923) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1922 &+ 1923 = 1 \end{align*} \begin{equation*} (1922\div 2)\times 1 + 1 = 962 \end{equation*}
Find the value of $1-2+3-4+\cdots+1923-1924+1925$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1924+1925) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1924 &+ 1925 = 1 \end{align*} \begin{equation*} (1924\div 2)\times 1 + 1 = 963 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1924+1925) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1924 &+ 1925 = 1 \end{align*} \begin{equation*} (1924\div 2)\times 1 + 1 = 963 \end{equation*}
Find the value of $1-2+3-4+\cdots+1925-1926+1927$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1926+1927) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1926 &+ 1927 = 1 \end{align*} \begin{equation*} (1926\div 2)\times 1 + 1 = 964 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1926+1927) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1926 &+ 1927 = 1 \end{align*} \begin{equation*} (1926\div 2)\times 1 + 1 = 964 \end{equation*}
Find the value of $1-2+3-4+\cdots+1927-1928+1929$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1928+1929) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1928 &+ 1929 = 1 \end{align*} \begin{equation*} (1928\div 2)\times 1 + 1 = 965 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1928+1929) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1928 &+ 1929 = 1 \end{align*} \begin{equation*} (1928\div 2)\times 1 + 1 = 965 \end{equation*}
Find the value of $1-2+3-4+\cdots+1929-1930+1931$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1930+1931) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1930 &+ 1931 = 1 \end{align*} \begin{equation*} (1930\div 2)\times 1 + 1 = 966 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1930+1931) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1930 &+ 1931 = 1 \end{align*} \begin{equation*} (1930\div 2)\times 1 + 1 = 966 \end{equation*}
Find the value of $1-2+3-4+\cdots+1931-1932+1933$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1932+1933) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1932 &+ 1933 = 1 \end{align*} \begin{equation*} (1932\div 2)\times 1 + 1 = 967 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1932+1933) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1932 &+ 1933 = 1 \end{align*} \begin{equation*} (1932\div 2)\times 1 + 1 = 967 \end{equation*}
Find the value of $1-2+3-4+\cdots+1933-1934+1935$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1934+1935) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1934 &+ 1935 = 1 \end{align*} \begin{equation*} (1934\div 2)\times 1 + 1 = 968 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1934+1935) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1934 &+ 1935 = 1 \end{align*} \begin{equation*} (1934\div 2)\times 1 + 1 = 968 \end{equation*}
Find the value of $1-2+3-4+\cdots+1935-1936+1937$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1936+1937) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1936 &+ 1937 = 1 \end{align*} \begin{equation*} (1936\div 2)\times 1 + 1 = 969 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1936+1937) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1936 &+ 1937 = 1 \end{align*} \begin{equation*} (1936\div 2)\times 1 + 1 = 969 \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*}
Yay! Your are right.
\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 $1-2+3-4+\cdots+1939-1940+1941$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1940+1941) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1940 &+ 1941 = 1 \end{align*} \begin{equation*} (1940\div 2)\times 1 + 1 = 971 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1940+1941) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1940 &+ 1941 = 1 \end{align*} \begin{equation*} (1940\div 2)\times 1 + 1 = 971 \end{equation*}
Find the value of $1-2+3-4+\cdots+1941-1942+1943$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1942+1943) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1942 &+ 1943 = 1 \end{align*} \begin{equation*} (1942\div 2)\times 1 + 1 = 972 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1942+1943) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1942 &+ 1943 = 1 \end{align*} \begin{equation*} (1942\div 2)\times 1 + 1 = 972 \end{equation*}
Find the value of $1-2+3-4+\cdots+1943-1944+1945$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1944+1945) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1944 &+ 1945 = 1 \end{align*} \begin{equation*} (1944\div 2)\times 1 + 1 = 973 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1944+1945) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1944 &+ 1945 = 1 \end{align*} \begin{equation*} (1944\div 2)\times 1 + 1 = 973 \end{equation*}
Find the value of $1-2+3-4+\cdots+1945-1946+1947$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1946+1947) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1946 &+ 1947 = 1 \end{align*} \begin{equation*} (1946\div 2)\times 1 + 1 = 974 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1946+1947) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1946 &+ 1947 = 1 \end{align*} \begin{equation*} (1946\div 2)\times 1 + 1 = 974 \end{equation*}
Find the value of $1-2+3-4+\cdots+1947-1948+1949$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1948+1949) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1948 &+ 1949 = 1 \end{align*} \begin{equation*} (1948\div 2)\times 1 + 1 = 975 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1948+1949) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1948 &+ 1949 = 1 \end{align*} \begin{equation*} (1948\div 2)\times 1 + 1 = 975 \end{equation*}
Find the value of $1-2+3-4+\cdots+1949-1950+1951$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1950+1951) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1950 &+ 1951 = 1 \end{align*} \begin{equation*} (1950\div 2)\times 1 + 1 = 976 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1950+1951) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1950 &+ 1951 = 1 \end{align*} \begin{equation*} (1950\div 2)\times 1 + 1 = 976 \end{equation*}
Find the value of $1-2+3-4+\cdots+1951-1952+1953$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1952+1953) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1952 &+ 1953 = 1 \end{align*} \begin{equation*} (1952\div 2)\times 1 + 1 = 977 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1952+1953) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1952 &+ 1953 = 1 \end{align*} \begin{equation*} (1952\div 2)\times 1 + 1 = 977 \end{equation*}
Find the value of $1-2+3-4+\cdots+1953-1954+1955$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1954+1955) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1954 &+ 1955 = 1 \end{align*} \begin{equation*} (1954\div 2)\times 1 + 1 = 978 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1954+1955) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1954 &+ 1955 = 1 \end{align*} \begin{equation*} (1954\div 2)\times 1 + 1 = 978 \end{equation*}
Find the value of $1-2+3-4+\cdots+1955-1956+1957$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1956+1957) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1956 &+ 1957 = 1 \end{align*} \begin{equation*} (1956\div 2)\times 1 + 1 = 979 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1956+1957) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1956 &+ 1957 = 1 \end{align*} \begin{equation*} (1956\div 2)\times 1 + 1 = 979 \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*}
Yay! Your are right.
\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 $1-2+3-4+\cdots+1959-1960+1961$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1960+1961) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1960 &+ 1961 = 1 \end{align*} \begin{equation*} (1960\div 2)\times 1 + 1 = 981 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1960+1961) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1960 &+ 1961 = 1 \end{align*} \begin{equation*} (1960\div 2)\times 1 + 1 = 981 \end{equation*}
Find the value of $1-2+3-4+\cdots+1961-1962+1963$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1962+1963) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1962 &+ 1963 = 1 \end{align*} \begin{equation*} (1962\div 2)\times 1 + 1 = 982 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1962+1963) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1962 &+ 1963 = 1 \end{align*} \begin{equation*} (1962\div 2)\times 1 + 1 = 982 \end{equation*}
Find the value of $1-2+3-4+\cdots+1963-1964+1965$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1964+1965) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1964 &+ 1965 = 1 \end{align*} \begin{equation*} (1964\div 2)\times 1 + 1 = 983 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1964+1965) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1964 &+ 1965 = 1 \end{align*} \begin{equation*} (1964\div 2)\times 1 + 1 = 983 \end{equation*}
Find the value of $1-2+3-4+\cdots+1965-1966+1967$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1966+1967) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1966 &+ 1967 = 1 \end{align*} \begin{equation*} (1966\div 2)\times 1 + 1 = 984 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1966+1967) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1966 &+ 1967 = 1 \end{align*} \begin{equation*} (1966\div 2)\times 1 + 1 = 984 \end{equation*}
Find the value of $1-2+3-4+\cdots+1967-1968+1969$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1968+1969) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1968 &+ 1969 = 1 \end{align*} \begin{equation*} (1968\div 2)\times 1 + 1 = 985 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1968+1969) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1968 &+ 1969 = 1 \end{align*} \begin{equation*} (1968\div 2)\times 1 + 1 = 985 \end{equation*}
Find the value of $1-2+3-4+\cdots+1969-1970+1971$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1970+1971) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1970 &+ 1971 = 1 \end{align*} \begin{equation*} (1970\div 2)\times 1 + 1 = 986 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1970+1971) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1970 &+ 1971 = 1 \end{align*} \begin{equation*} (1970\div 2)\times 1 + 1 = 986 \end{equation*}
Find the value of $1-2+3-4+\cdots+1971-1972+1973$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1972+1973) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1972 &+ 1973 = 1 \end{align*} \begin{equation*} (1972\div 2)\times 1 + 1 = 987 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1972+1973) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1972 &+ 1973 = 1 \end{align*} \begin{equation*} (1972\div 2)\times 1 + 1 = 987 \end{equation*}
Find the value of $1-2+3-4+\cdots+1973-1974+1975$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1974+1975) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1974 &+ 1975 = 1 \end{align*} \begin{equation*} (1974\div 2)\times 1 + 1 = 988 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1974+1975) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1974 &+ 1975 = 1 \end{align*} \begin{equation*} (1974\div 2)\times 1 + 1 = 988 \end{equation*}
Find the value of $1-2+3-4+\cdots+1975-1976+1977$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1976+1977) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1976 &+ 1977 = 1 \end{align*} \begin{equation*} (1976\div 2)\times 1 + 1 = 989 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1976+1977) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1976 &+ 1977 = 1 \end{align*} \begin{equation*} (1976\div 2)\times 1 + 1 = 989 \end{equation*}
Find the value of $1-2+3-4+\cdots+1977-1978+1979$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1978+1979) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1978 &+ 1979 = 1 \end{align*} \begin{equation*} (1978\div 2)\times 1 + 1 = 990 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1978+1979) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1978 &+ 1979 = 1 \end{align*} \begin{equation*} (1978\div 2)\times 1 + 1 = 990 \end{equation*}
Find the value of $1-2+3-4+\cdots+1979-1980+1981$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1980+1981) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1980 &+ 1981 = 1 \end{align*} \begin{equation*} (1980\div 2)\times 1 + 1 = 991 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1980+1981) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1980 &+ 1981 = 1 \end{align*} \begin{equation*} (1980\div 2)\times 1 + 1 = 991 \end{equation*}
Find the value of $1-2+3-4+\cdots+1981-1982+1983$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1982+1983) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1982 &+ 1983 = 1 \end{align*} \begin{equation*} (1982\div 2)\times 1 + 1 = 992 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1982+1983) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1982 &+ 1983 = 1 \end{align*} \begin{equation*} (1982\div 2)\times 1 + 1 = 992 \end{equation*}
Find the value of $1-2+3-4+\cdots+1983-1984+1985$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1984+1985) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1984 &+ 1985 = 1 \end{align*} \begin{equation*} (1984\div 2)\times 1 + 1 = 993 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1984+1985) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1984 &+ 1985 = 1 \end{align*} \begin{equation*} (1984\div 2)\times 1 + 1 = 993 \end{equation*}
Find the value of $1-2+3-4+\cdots+1985-1986+1987$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1986+1987) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1986 &+ 1987 = 1 \end{align*} \begin{equation*} (1986\div 2)\times 1 + 1 = 994 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1986+1987) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1986 &+ 1987 = 1 \end{align*} \begin{equation*} (1986\div 2)\times 1 + 1 = 994 \end{equation*}
Find the value of $1-2+3-4+\cdots+1987-1988+1989$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1988+1989) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1988 &+ 1989 = 1 \end{align*} \begin{equation*} (1988\div 2)\times 1 + 1 = 995 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1988+1989) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1988 &+ 1989 = 1 \end{align*} \begin{equation*} (1988\div 2)\times 1 + 1 = 995 \end{equation*}
Find the value of $1-2+3-4+\cdots+1989-1990+1991$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1990+1991) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1990 &+ 1991 = 1 \end{align*} \begin{equation*} (1990\div 2)\times 1 + 1 = 996 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1990+1991) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1990 &+ 1991 = 1 \end{align*} \begin{equation*} (1990\div 2)\times 1 + 1 = 996 \end{equation*}
Find the value of $1-2+3-4+\cdots+1991-1992+1993$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1992+1993) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1992 &+ 1993 = 1 \end{align*} \begin{equation*} (1992\div 2)\times 1 + 1 = 997 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1992+1993) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1992 &+ 1993 = 1 \end{align*} \begin{equation*} (1992\div 2)\times 1 + 1 = 997 \end{equation*}
Find the value of $1-2+3-4+\cdots+1993-1994+1995$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1994+1995) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1994 &+ 1995 = 1 \end{align*} \begin{equation*} (1994\div 2)\times 1 + 1 = 998 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1994+1995) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1994 &+ 1995 = 1 \end{align*} \begin{equation*} (1994\div 2)\times 1 + 1 = 998 \end{equation*}
Find the value of $1-2+3-4+\cdots+1995-1996+1997$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1996+1997) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1996 &+ 1997 = 1 \end{align*} \begin{equation*} (1996\div 2)\times 1 + 1 = 999 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-1996+1997) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -1996 &+ 1997 = 1 \end{align*} \begin{equation*} (1996\div 2)\times 1 + 1 = 999 \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*}
Yay! Your are right.
\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 $1-2+3-4+\cdots+1999-2000+2001$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2000+2001) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2000 &+ 2001 = 1 \end{align*} \begin{equation*} (2000\div 2)\times 1 + 1 = 1001 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2000+2001) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2000 &+ 2001 = 1 \end{align*} \begin{equation*} (2000\div 2)\times 1 + 1 = 1001 \end{equation*}
Find the value of $1-2+3-4+\cdots+2001-2002+2003$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2002+2003) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2002 &+ 2003 = 1 \end{align*} \begin{equation*} (2002\div 2)\times 1 + 1 = 1002 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2002+2003) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2002 &+ 2003 = 1 \end{align*} \begin{equation*} (2002\div 2)\times 1 + 1 = 1002 \end{equation*}
Find the value of $1-2+3-4+\cdots+2003-2004+2005$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2004+2005) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2004 &+ 2005 = 1 \end{align*} \begin{equation*} (2004\div 2)\times 1 + 1 = 1003 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2004+2005) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2004 &+ 2005 = 1 \end{align*} \begin{equation*} (2004\div 2)\times 1 + 1 = 1003 \end{equation*}
Find the value of $1-2+3-4+\cdots+2005-2006+2007$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2006+2007) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2006 &+ 2007 = 1 \end{align*} \begin{equation*} (2006\div 2)\times 1 + 1 = 1004 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2006+2007) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2006 &+ 2007 = 1 \end{align*} \begin{equation*} (2006\div 2)\times 1 + 1 = 1004 \end{equation*}
Find the value of $1-2+3-4+\cdots+2007-2008+2009$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2008+2009) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2008 &+ 2009 = 1 \end{align*} \begin{equation*} (2008\div 2)\times 1 + 1 = 1005 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2008+2009) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2008 &+ 2009 = 1 \end{align*} \begin{equation*} (2008\div 2)\times 1 + 1 = 1005 \end{equation*}
Find the value of $1-2+3-4+\cdots+2009-2010+2011$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2010+2011) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2010 &+ 2011 = 1 \end{align*} \begin{equation*} (2010\div 2)\times 1 + 1 = 1006 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2010+2011) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2010 &+ 2011 = 1 \end{align*} \begin{equation*} (2010\div 2)\times 1 + 1 = 1006 \end{equation*}
Find the value of $1-2+3-4+\cdots+2011-2012+2013$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2012+2013) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2012 &+ 2013 = 1 \end{align*} \begin{equation*} (2012\div 2)\times 1 + 1 = 1007 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2012+2013) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2012 &+ 2013 = 1 \end{align*} \begin{equation*} (2012\div 2)\times 1 + 1 = 1007 \end{equation*}
Find the value of $1-2+3-4+\cdots+2013-2014+2015$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2014+2015) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2014 &+ 2015 = 1 \end{align*} \begin{equation*} (2014\div 2)\times 1 + 1 = 1008 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2014+2015) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2014 &+ 2015 = 1 \end{align*} \begin{equation*} (2014\div 2)\times 1 + 1 = 1008 \end{equation*}
Find the value of $1-2+3-4+\cdots+2017-2018+2019$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2018+2019) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2018 &+ 2019 = 1 \end{align*} \begin{equation*} (2018\div 2)\times 1 + 1 = 1010 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2018+2019) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2018 &+ 2019 = 1 \end{align*} \begin{equation*} (2018\div 2)\times 1 + 1 = 1010 \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*}
Yay! Your are right.
\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 $1-2+3-4+\cdots+2021-2022+2023$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2022+2023) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2022 &+ 2023 = 1 \end{align*} \begin{equation*} (2022\div 2)\times 1 + 1 = 1012 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2022+2023) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2022 &+ 2023 = 1 \end{align*} \begin{equation*} (2022\div 2)\times 1 + 1 = 1012 \end{equation*}
Find the value of $1-2+3-4+\cdots+2023-2024+2025$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2024+2025) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2024 &+ 2025 = 1 \end{align*} \begin{equation*} (2024\div 2)\times 1 + 1 = 1013 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2024+2025) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2024 &+ 2025 = 1 \end{align*} \begin{equation*} (2024\div 2)\times 1 + 1 = 1013 \end{equation*}
Find the value of $1-2+3-4+\cdots+2025-2026+2027$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2026+2027) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2026 &+ 2027 = 1 \end{align*} \begin{equation*} (2026\div 2)\times 1 + 1 = 1014 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2026+2027) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2026 &+ 2027 = 1 \end{align*} \begin{equation*} (2026\div 2)\times 1 + 1 = 1014 \end{equation*}
Find the value of $1-2+3-4+\cdots+2027-2028+2029$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2028+2029) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2028 &+ 2029 = 1 \end{align*} \begin{equation*} (2028\div 2)\times 1 + 1 = 1015 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2028+2029) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2028 &+ 2029 = 1 \end{align*} \begin{equation*} (2028\div 2)\times 1 + 1 = 1015 \end{equation*}
Find the value of $1-2+3-4+\cdots+2029-2030+2031$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2030+2031) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2030 &+ 2031 = 1 \end{align*} \begin{equation*} (2030\div 2)\times 1 + 1 = 1016 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2030+2031) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2030 &+ 2031 = 1 \end{align*} \begin{equation*} (2030\div 2)\times 1 + 1 = 1016 \end{equation*}
Find the value of $1-2+3-4+\cdots+2031-2032+2033$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2032+2033) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2032 &+ 2033 = 1 \end{align*} \begin{equation*} (2032\div 2)\times 1 + 1 = 1017 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2032+2033) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2032 &+ 2033 = 1 \end{align*} \begin{equation*} (2032\div 2)\times 1 + 1 = 1017 \end{equation*}
Find the value of $1-2+3-4+\cdots+2033-2034+2035$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2034+2035) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2034 &+ 2035 = 1 \end{align*} \begin{equation*} (2034\div 2)\times 1 + 1 = 1018 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2034+2035) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2034 &+ 2035 = 1 \end{align*} \begin{equation*} (2034\div 2)\times 1 + 1 = 1018 \end{equation*}
Find the value of $1-2+3-4+\cdots+2035-2036+2037$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2036+2037) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2036 &+ 2037 = 1 \end{align*} \begin{equation*} (2036\div 2)\times 1 + 1 = 1019 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2036+2037) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2036 &+ 2037 = 1 \end{align*} \begin{equation*} (2036\div 2)\times 1 + 1 = 1019 \end{equation*}
Find the value of $1-2+3-4+\cdots+2037-2038+2039$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2038+2039) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2038 &+ 2039 = 1 \end{align*} \begin{equation*} (2038\div 2)\times 1 + 1 = 1020 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2038+2039) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2038 &+ 2039 = 1 \end{align*} \begin{equation*} (2038\div 2)\times 1 + 1 = 1020 \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*}
Yay! Your are right.
\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 $1-2+3-4+\cdots+2041-2042+2043$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2042+2043) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2042 &+ 2043 = 1 \end{align*} \begin{equation*} (2042\div 2)\times 1 + 1 = 1022 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2042+2043) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2042 &+ 2043 = 1 \end{align*} \begin{equation*} (2042\div 2)\times 1 + 1 = 1022 \end{equation*}
Find the value of $1-2+3-4+\cdots+2043-2044+2045$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2044+2045) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2044 &+ 2045 = 1 \end{align*} \begin{equation*} (2044\div 2)\times 1 + 1 = 1023 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2044+2045) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2044 &+ 2045 = 1 \end{align*} \begin{equation*} (2044\div 2)\times 1 + 1 = 1023 \end{equation*}
Find the value of $1-2+3-4+\cdots+2045-2046+2047$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2046+2047) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2046 &+ 2047 = 1 \end{align*} \begin{equation*} (2046\div 2)\times 1 + 1 = 1024 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2046+2047) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2046 &+ 2047 = 1 \end{align*} \begin{equation*} (2046\div 2)\times 1 + 1 = 1024 \end{equation*}
Find the value of $1-2+3-4+\cdots+2047-2048+2049$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2048+2049) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2048 &+ 2049 = 1 \end{align*} \begin{equation*} (2048\div 2)\times 1 + 1 = 1025 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2048+2049) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2048 &+ 2049 = 1 \end{align*} \begin{equation*} (2048\div 2)\times 1 + 1 = 1025 \end{equation*}
Find the value of $1-2+3-4+\cdots+2049-2050+2051$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2050+2051) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2050 &+ 2051 = 1 \end{align*} \begin{equation*} (2050\div 2)\times 1 + 1 = 1026 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2050+2051) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2050 &+ 2051 = 1 \end{align*} \begin{equation*} (2050\div 2)\times 1 + 1 = 1026 \end{equation*}
Find the value of $1-2+3-4+\cdots+2051-2052+2053$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2052+2053) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2052 &+ 2053 = 1 \end{align*} \begin{equation*} (2052\div 2)\times 1 + 1 = 1027 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2052+2053) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2052 &+ 2053 = 1 \end{align*} \begin{equation*} (2052\div 2)\times 1 + 1 = 1027 \end{equation*}
Find the value of $1-2+3-4+\cdots+2053-2054+2055$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2054+2055) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2054 &+ 2055 = 1 \end{align*} \begin{equation*} (2054\div 2)\times 1 + 1 = 1028 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2054+2055) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2054 &+ 2055 = 1 \end{align*} \begin{equation*} (2054\div 2)\times 1 + 1 = 1028 \end{equation*}
Find the value of $1-2+3-4+\cdots+2055-2056+2057$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2056+2057) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2056 &+ 2057 = 1 \end{align*} \begin{equation*} (2056\div 2)\times 1 + 1 = 1029 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2056+2057) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2056 &+ 2057 = 1 \end{align*} \begin{equation*} (2056\div 2)\times 1 + 1 = 1029 \end{equation*}
Find the value of $1-2+3-4+\cdots+2057-2058+2059$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2058+2059) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2058 &+ 2059 = 1 \end{align*} \begin{equation*} (2058\div 2)\times 1 + 1 = 1030 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2058+2059) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2058 &+ 2059 = 1 \end{align*} \begin{equation*} (2058\div 2)\times 1 + 1 = 1030 \end{equation*}
Find the value of $1-2+3-4+\cdots+2059-2060+2061$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2060+2061) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2060 &+ 2061 = 1 \end{align*} \begin{equation*} (2060\div 2)\times 1 + 1 = 1031 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2060+2061) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2060 &+ 2061 = 1 \end{align*} \begin{equation*} (2060\div 2)\times 1 + 1 = 1031 \end{equation*}
Find the value of $1-2+3-4+\cdots+2061-2062+2063$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2062+2063) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2062 &+ 2063 = 1 \end{align*} \begin{equation*} (2062\div 2)\times 1 + 1 = 1032 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2062+2063) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2062 &+ 2063 = 1 \end{align*} \begin{equation*} (2062\div 2)\times 1 + 1 = 1032 \end{equation*}
Find the value of $1-2+3-4+\cdots+2063-2064+2065$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2064+2065) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2064 &+ 2065 = 1 \end{align*} \begin{equation*} (2064\div 2)\times 1 + 1 = 1033 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2064+2065) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2064 &+ 2065 = 1 \end{align*} \begin{equation*} (2064\div 2)\times 1 + 1 = 1033 \end{equation*}
Find the value of $1-2+3-4+\cdots+2065-2066+2067$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2066+2067) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2066 &+ 2067 = 1 \end{align*} \begin{equation*} (2066\div 2)\times 1 + 1 = 1034 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2066+2067) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2066 &+ 2067 = 1 \end{align*} \begin{equation*} (2066\div 2)\times 1 + 1 = 1034 \end{equation*}
Find the value of $1-2+3-4+\cdots+2067-2068+2069$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2068+2069) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2068 &+ 2069 = 1 \end{align*} \begin{equation*} (2068\div 2)\times 1 + 1 = 1035 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2068+2069) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2068 &+ 2069 = 1 \end{align*} \begin{equation*} (2068\div 2)\times 1 + 1 = 1035 \end{equation*}
Find the value of $1-2+3-4+\cdots+2069-2070+2071$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2070+2071) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2070 &+ 2071 = 1 \end{align*} \begin{equation*} (2070\div 2)\times 1 + 1 = 1036 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2070+2071) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2070 &+ 2071 = 1 \end{align*} \begin{equation*} (2070\div 2)\times 1 + 1 = 1036 \end{equation*}
Find the value of $1-2+3-4+\cdots+2071-2072+2073$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2072+2073) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2072 &+ 2073 = 1 \end{align*} \begin{equation*} (2072\div 2)\times 1 + 1 = 1037 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2072+2073) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2072 &+ 2073 = 1 \end{align*} \begin{equation*} (2072\div 2)\times 1 + 1 = 1037 \end{equation*}
Find the value of $1-2+3-4+\cdots+2073-2074+2075$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2074+2075) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2074 &+ 2075 = 1 \end{align*} \begin{equation*} (2074\div 2)\times 1 + 1 = 1038 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2074+2075) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2074 &+ 2075 = 1 \end{align*} \begin{equation*} (2074\div 2)\times 1 + 1 = 1038 \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 $1-2+3-4+\cdots+2077-2078+2079$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2078+2079) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2078 &+ 2079 = 1 \end{align*} \begin{equation*} (2078\div 2)\times 1 + 1 = 1040 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2078+2079) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2078 &+ 2079 = 1 \end{align*} \begin{equation*} (2078\div 2)\times 1 + 1 = 1040 \end{equation*}
Find the value of $1-2+3-4+\cdots+2079-2080+2081$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2080+2081) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2080 &+ 2081 = 1 \end{align*} \begin{equation*} (2080\div 2)\times 1 + 1 = 1041 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2080+2081) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2080 &+ 2081 = 1 \end{align*} \begin{equation*} (2080\div 2)\times 1 + 1 = 1041 \end{equation*}
Find the value of $1-2+3-4+\cdots+2081-2082+2083$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2082+2083) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2082 &+ 2083 = 1 \end{align*} \begin{equation*} (2082\div 2)\times 1 + 1 = 1042 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2082+2083) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2082 &+ 2083 = 1 \end{align*} \begin{equation*} (2082\div 2)\times 1 + 1 = 1042 \end{equation*}
Find the value of $1-2+3-4+\cdots+2083-2084+2085$.
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\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2084+2085) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2084 &+ 2085 = 1 \end{align*} \begin{equation*} (2084\div 2)\times 1 + 1 = 1043 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2084+2085) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2084 &+ 2085 = 1 \end{align*} \begin{equation*} (2084\div 2)\times 1 + 1 = 1043 \end{equation*}
Find the value of $1-2+3-4+\cdots+2085-2086+2087$.
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Sorry. Please check the correct answer below.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2086+2087) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2086 &+ 2087 = 1 \end{align*} \begin{equation*} (2086\div 2)\times 1 + 1 = 1044 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2086+2087) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2086 &+ 2087 = 1 \end{align*} \begin{equation*} (2086\div 2)\times 1 + 1 = 1044 \end{equation*}
Find the value of $1-2+3-4+\cdots+2087-2088+2089$.
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Sorry. Please check the correct answer below.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2088+2089) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2088 &+ 2089 = 1 \end{align*} \begin{equation*} (2088\div 2)\times 1 + 1 = 1045 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2088+2089) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2088 &+ 2089 = 1 \end{align*} \begin{equation*} (2088\div 2)\times 1 + 1 = 1045 \end{equation*}
Find the value of $1-2+3-4+\cdots+2089-2090+2091$.
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Sorry. Please check the correct answer below.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2090+2091) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2090 &+ 2091 = 1 \end{align*} \begin{equation*} (2090\div 2)\times 1 + 1 = 1046 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2090+2091) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2090 &+ 2091 = 1 \end{align*} \begin{equation*} (2090\div 2)\times 1 + 1 = 1046 \end{equation*}
Find the value of $1-2+3-4+\cdots+2091-2092+2093$.
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Sorry. Please check the correct answer below.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2092+2093) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2092 &+ 2093 = 1 \end{align*} \begin{equation*} (2092\div 2)\times 1 + 1 = 1047 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2092+2093) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2092 &+ 2093 = 1 \end{align*} \begin{equation*} (2092\div 2)\times 1 + 1 = 1047 \end{equation*}
Find the value of $1-2+3-4+\cdots+2093-2094+2095$.
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Sorry. Please check the correct answer below.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2094+2095) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2094 &+ 2095 = 1 \end{align*} \begin{equation*} (2094\div 2)\times 1 + 1 = 1048 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2094+2095) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2094 &+ 2095 = 1 \end{align*} \begin{equation*} (2094\div 2)\times 1 + 1 = 1048 \end{equation*}
Find the value of $1-2+3-4+\cdots+2095-2096+2097$.
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Sorry. Please check the correct answer below.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2096+2097) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2096 &+ 2097 = 1 \end{align*} \begin{equation*} (2096\div 2)\times 1 + 1 = 1049 \end{equation*}
Yay! Your are right.
\begin{equation*} 1+(-2+3)+(-4+5)+\cdots+(-2096+2097) \end{equation*} \begin{align*} -2+3 &= 3-2 = 1 \\ -4+5 &= 5-4 = 1 \\ & \hspace{2.5mm} \vdots \\ \ -2096 &+ 2097 = 1 \end{align*} \begin{equation*} (2096\div 2)\times 1 + 1 = 1049 \end{equation*}
Find the value of $1-2+3-4+\cdots+2097-2098+2099$.
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Sorry. Please check the correct answer below.
\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*}
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