If $\sum a_n$ converges where $a_n \ge 0 \; \forall \; n \in \Bbb N$, then $\{n a_n\}$ converges or diverges?
Is it possible that $a_n>0$ and $\sum a_n$ converges then $na_n \to 0$? (without assuming $a_n$ is decreasing)