\(\frac{1}{2}\)+\(\frac{1}{6}\)+\(\frac{1}{12}\)+....+\(\frac{1}{x\left(x+1\right)}\)=\(\frac{2015}{2016}\)
\(\frac{1}{1x2}\)+\(\frac{1}{2x3}\)+\(\frac{1}{3x4}\)+.....+\(\frac{1}{x\left(x+1\right)}\)=\(\frac{2015}{2016}\)
\(1\)-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-.....+\(\frac{1}{x}\)-\(\frac{1}{x+1}\)=\(\frac{2015}{2016}\)
1-\(\frac{1}{x+1}\) = \(\frac{2015}{2016}\)
\(\frac{1}{x+1}\) =1- \(\frac{2015}{2016}\)
\(\frac{1}{x+1}\) = \(\frac{1}{2016}\)
\(\Rightarrow\)x + 1= 2016
\(\Rightarrow\)x = 2015