Question

Aratati ca 1/1*2+1/2*3+...+1/2011*2012<1.

Answer 1

$\frac{1}{1*2} + \frac{1}{2*3} +....+ \frac{1}{2011*2012} \ \textless \ 1 \\ \\ \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} +.....+ \frac{1}{2011} - \frac{1}{2012} \ \textless \ 1 \\ \\ \frac{1}{1} - \frac{1}{2012} \ \textless \ 1 \\ \\ \frac{2012}{2012}- \frac{1}{2012}\ \textless \ 1 \\ \\ \frac{2011}{2012} \ \textless \ 1$