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China Mathematics Olympiads (National Round) 2007 Problem 5

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November 28, 2010
algebra unsolvedalgebra

Problem Statement

Let {an}n≥1\{a_n\}_{n \geq 1} be a bounded sequence satisfying a_n < \displaystyle\sum_{k=a}^{2n+2006} \frac{a_k}{k+1} + \frac{1}{2n+2007}   \forall   n = 1, 2, 3, \ldots Show that a_n < \frac{1}{n}   \forall   n = 1, 2, 3, \ldots
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