If $\displaystyle \sum ^\infty _{n=1} a_n$ converges and $\displaystyle a_n>0, \forall n \in \mathbb{N}$ , than does$\displaystyle \sum ^\infty _{n=1} \frac{\sqrt{a_n}}{n}$ converges??

I think it converges, but I don't know if I am right, or how to prove it.