Question

C=(1+1/1x3)x(1+1/2x4)x(1+1/3x5)x.....x(1+1/2014x2016)
C=....

Answer 1

\(C=\dfrac{2^2-1+1}{\left(2-1\right)\left(2+1\right)}\cdot\dfrac{3^2-1+1}{\left(3-1\right)\left(3+1\right)}\cdot...\cdot\dfrac{2015^2-1+1}{\left(2015-1\right)\left(2015+1\right)}\)

\(=\dfrac{2}{1}\cdot\dfrac{3}{2}\cdot...\cdot\dfrac{2015}{2014}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2015}{2016}\)

=2015/1*2/2016=2015/1008