[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 .

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