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2014 IMO Problems/Problem 1

Revision as of 04:12, 9 October 2014 by Timneh (talk | contribs) (Created page with "==Problem== Let <math>a__0<a_1<a_2<\cdots \quad </math> be an infinite sequence of positive integers, Prove that there exists a unique integer <math>n\ge1</math> such that <cmat...")
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Problem

Let $a__0<a_1<a_2<\cdots \quad$ (Error compiling LaTeX. Unknown error_msg) be an infinite sequence of positive integers, Prove that there exists a unique integer $n\ge1$ such that \[a_n<\frac{a_0+a_1+\cdots + a_n}{n}\le a_{n+1}.\]

Solution

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