# 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 $$a_n<\frac{a_0+a_1+\cdots + a_n}{n}\le a_{n+1}.$$