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IMO LongList 1987 - Inequality on 1987 positive reals

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September 6, 2010
inequalitiesinequalities unsolved

Problem Statement

Let aka_k be positive numbers such that a1≥1a_1 \geq 1 and ak+1−ak≥1 (k=1,2,...)a_{k+1} -a_k \geq 1 \ (k = 1, 2, . . . ). Prove that for every n∈N,n \in \mathbb N, ∑k=119871ak+1ak1987<1987\sum_{k=1}^{1987}\frac{1}{a_{k+1} \sqrt[1987]{a_k}} <1987
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