VTRMC 2010 Problem 7

Let $\sum_{n=1}^\infty a_n$ be a convergent series of positive terms (so $a_i>0$ for all $i$ ) and set $b_n=\frac1{na_n^2}$ for $n\ge1$ . Prove that $\sum_{n=1}^\infty\frac n{b_1+b_2+\ldots+b_n}$ is convergent.