Show that $\sum_{n=1}^\infty\frac{\sqrt{a_n}}{n^p}$ converges for p > $\frac{1}{2}$ [duplicate]

Let $\sum_{n=1}^\infty{a_n}{}$ be a convergent series of positive terms.

Show that $$\sum_{n=1}^\infty\frac{\sqrt{a_n}}{n^p}$$

converges for p > $\frac{1}{2}$

-

marked as duplicate by 23rd, Thomas Andrews, Davide Giraudo, O.L., Nicholas R. PetersonAug 3 '13 at 12:59

Hint: by arithmetic-geometric mean, we have $$\frac {\sqrt{a_n}} {n^p} \leq a_n + \frac{1}{n^{2p}}.$$