Question

Answer 1

\(=2\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{2012.2014}+\dfrac{2}{2014.2016}\right)\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2012}-\dfrac{1}{2014}+\dfrac{1}{2014}-\dfrac{1}{2016}\right)\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{2016}\right)\)

\(=1-\dfrac{1}{1008}=\dfrac{1007}{1008}\)

Answer 2

=1007/1008

Answer 3

2x( 2/2.4 + 2/4.6 +...+ 2/2014.2016) = 2x( 1/2-1/4+1/4-1/6+...+1/2014-1/2016)=
2x(1/2-1/2016)=1-1/1008=1007/1008