# Difference between revisions of "2014 IMO Problems/Problem 1"

## Problem

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

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.

## See Also

 2014 IMO (Problems) • Resources Preceded byFirst Problem 1 • 2 • 3 • 4 • 5 • 6 Followed byProblem 2 All IMO Problems and Solutions

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