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Let
be an infinite sequence of positive integers. Prove that there exists a unique integer
such that
![\[a_n < \frac{a_0+a_1+a_2+\cdots+a_n}{n} \leq a_{n+1}.\]](//latex.artofproblemsolving.com/9/4/f/94fc5a51b7e68588123c5b527fe75183bc4c4937.png)
Proposed by Gerhard Wöginger, Austria.


![\[a_n < \frac{a_0+a_1+a_2+\cdots+a_n}{n} \leq a_{n+1}.\]](http://latex.artofproblemsolving.com/9/4/f/94fc5a51b7e68588123c5b527fe75183bc4c4937.png)
Proposed by Gerhard Wöginger, Austria.
This post has been edited 1 time. Last edited by v_Enhance, Nov 5, 2023, 5:17 PM
Reason: missing < sign
Reason: missing < sign