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Is there a lower boundary for a fraction sum inequality?

Source: IMO LongList 1988, Vietnam 4, Problem 92 of ILL

November 9, 2005
inequalitiesalgebra unsolvedalgebra

Problem Statement

Let p≥2p \geq 2 be a natural number. Prove that there exist an integer n0n_0 such that ∑i=1n01i⋅i+1p>p. \sum^{n_0}_{i=1} \frac{1}{i \cdot \sqrt[p]{i + 1}} > p.
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