Need to prove: $\sum_{n=1}^{\infty}{a_n}$ converges $\implies\sum_{n=1}^{\infty }\frac{\sqrt{a_n}}{n}$ converges
If $\sum_{n=1}^{\infty} a_n^{2}$ converges, then so does $\sum_{n=1}^{\infty} \frac {a_n}{n}$