Question

A=1/1*2 + 1/2*3 + 1/3*4 +...+1/2015*2016

Answer 1

A = 1/1.2 + 1/2.3 + 1/3.4 + .... + 1/2015.2016

A = 1 - 1/2+1/2-1/3+1/3-1/4+...+1/2015-1/2016

A= 1 - 1/2016

A = 2015/2016

Answer 2

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...\frac{1}{2015.2016}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...\frac{1}{2015}-\frac{1}{2016}\)

\(=\frac{1}{1}-\frac{1}{2016}\)

\(=\frac{2015}{2016}\)