92

Part of 1988 IMO Longlists

Problems(1)

Is there a lower boundary for a fraction sum inequality?

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

p \geq 2

be a natural number. Prove that there exist an integer

n_0

\sum^{n_0}_{i=1} \frac{1}{i \cdot \sqrt[p]{i + 1}} > p.

inequalitiesalgebra unsolvedalgebra