Question

Tính A=(1/2^2-1)(1/3^2-1).....(1/2015^2-1)

Answer 1

\(A=\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+\frac{1}{4.6}+..........+\frac{1}{2013.2015}+\frac{1}{2014.2016}\)

\(=\left(\frac{1}{1.3}+\frac{1}{3.5}+......+\frac{1}{2013.2015}\right)+\left(\frac{1}{2.4}+\frac{1}{4.6}+......+\frac{1}{2014.2016}\right)\)

\(2A=\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2013}-\frac{1}{2015}\right)+\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)

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

A= 3/4 -1/4030  - 1/ 4032