S = 1/2 - 1/3 + 1/3 -1/4 + ......... +1/2011 -1/2012
S= 1/2 - 1/2012 = 1005/2012
\(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...-\frac{1}{2012}\)
\(S=\frac{1}{2}+0+0+0+...-\frac{1}{2012}\)
\(S=\frac{1}{2}-\frac{1}{2012}\)
\(S=\frac{1005}{2012}\)
\(A=\frac{2012}{1}\cdot\frac{1005}{2012}\)
\(A=1005\)
\(\Leftrightarrow S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{2011}-\frac{1}{2012}\)
\(\Rightarrow S=\frac{1}{2}-\frac{1}{2012}=\frac{1005}{2012}\)
=>A=\(\frac{2012\cdot1005}{1\cdot2012}=\frac{1005}{1}=1005\)
