Let $a_{n} > 0$ and $\sum a_{n}$ converges. Prove that $\forall p > \frac{1}{2}$ , $\sum \frac{\sqrt{a_{n}}}{n^{p}}$ converges. [duplicate]

Question

Let $a_{n} > 0$ and $\sum a_{n}$ converges. Prove that $\forall p > \frac{1}{2}$, $\sum \frac{\sqrt{a_{n}}}{n^{p}}$ converges.

Attempt.

Since, $\lim_{n \to \infty}a_{n} = 0$. After certain $n$ all the terms in the sequence $a_{n}$ will be less than 1. Thus I am not able to apply comparison test fruitfully here. Every approach that I am trying is facing the issue that $\sqrt{a_{n}} > a_{n}$. I have the intuition that somehow I have to use $n^{p}$ in the denominator so that comparison test can be applied. But I am not able to do so. Please help.