## [Hints] 2015 Kazakhstan NMO Problem 1

2015 Kazakh NMO 1. Prove that

$\displaystyle\frac{1}{2^2} + \frac{1}{3^2} + \dots + \frac{1}{(n+1)^2} < n\left( 1 - \frac{1}{\sqrt[n]{2}} \right)$

Hint: Look at the $n^{th}$ root. Does that remind you of some inequality? Try to rearrange the given inequality so that it looks like that that famous inequality .