Question

Tinh A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2014.2015}\)

 

Answer 1

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2014}-\frac{1}{2015}\)

\(=1-\frac{1}{2015}\)

\(=\frac{2014}{2015}\)

Answer 2

A=1/1-1/2+1/2-1/3+1/3-...........+1/2014-1/2015

A=1/1-1/2015

A=2014/2015