Question

Answer 1

\(A=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{2011\cdot2013}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2011}-\dfrac{1}{2013}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2012}{2013}=\dfrac{1006}{2013}\)

Answer 2

A=1/2(2/1⋅3+2/3⋅5+...+2/2011⋅2013)

A=1/2(1−1/3+1/3−1/5+...+1/2011−1/2013)

A=1/2⋅2012/2013

A=1006/2013