Absolute convergence of $\sum_{n=1}^{\infty}z_n^2$ There are two complex series given ($z \in \mathbb{C}$.
We know that: 
$$\sum_{n=1}^{\infty}z_n^2$$
converges absolutely.
We are to show that 
$$\sum_{n=1}^{\infty} \frac{z_n}{n}$$
also converges absolutely.
I tried to prove it with no success unfortunately. How should the proof look like?

This follows from Cauchy-Schwarz, applied to $\sum |z_n|^2$ and $\sum 1/n^2$.
