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Kazakhstan Contests
Kazakhstan National Olympiad
2015 Kazakhstan National Olympiad
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1
Part of
2015 Kazakhstan National Olympiad
Problems
(1)
Bounding the sum of squares of reciprocals
Source:
1/9/2015
Prove that
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\frac{1}{2^2}+\frac{1}{3^2}+\cdots+\frac{1}{(n+1)^2} < n \cdot \left(1-\frac{1}{\sqrt[n]{2}}\right).
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inequalities
inequalities proposed
Kazakhstan