# CGMO – 2012 ( China Girls Math Olympiad 2012 ) Problem 7

Let  $\{a_n\}$ be a sequence of nondecreasing positive integers such that  $\frac{r}{a_{r}}= k+1$ for some positive integers $k$ and $r$. Prove that there exists a positive integer $s$ such that  $\frac{s}{a_s} = k$