Question

\(\frac{1}{1x2}\)+ \(\frac{1}{2x3}\)+ ....... + \(\frac{1}{2015x2016}\)

 

 

Answer 1

\(\frac{1}{1\times2}+\frac{1}{2\times3}+.......+\frac{1}{2015\times2016}\)

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

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

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

Answer 2

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

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

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