Convergence of a series implies another convergence

Question

Assume that $\sum a_n$ converges and $a_n\geq 0$. Show that $\sum \dfrac{\sqrt{a_n}}{n}$ also converges. I tried using the comparison test but it does not necessarily work since $a_n$ may be less than 1. I think of using the partial summation formula but I cannot see how to make it work. Any help will do. Thanks!