Problem:
Suppose that for every $n\in\mathbb{N}$, $a_n\in\mathbb{R}$ and $a_n\ge 0$. Given that $\sum_0^\infty a_n$ converges, show that $\sum_1^\infty \frac{\sqrt{a_n}}{n} $ converges.
Source: Rudin, Principles of Mathematical Analysis, Chapter 3, Exercise 7.