2014 IMO Problems/Problem 1
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 
such that
![\[a_n<\frac{a_0+a_1+\cdots + a_n}{n}\le a_{n+1}.\]](http://latex.artofproblemsolving.com/0/c/4/0c463e53d0ab2ad520551056d74fad908d859cb5.png)
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 by First Problem |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
| All IMO Problems and Solutions | ||
