Convergence of $\sum_{n = 1}^\infty \frac{1}{z-n^2}$ I try to show that the following series converges for all $z \in \mathbb C$ (except the obvious poles). 
$$\sum_{n = 1}^\infty \frac{1}{z-n^2}$$
Since we have $n^2$ in the denominator I tried to use comparision test, but I couldn't achieve a suitable inequality (even tried to transform the fraction in a geometric series, but it didn't help). I would appreciate some help :)

Hint: Try showing that $|\frac{1}{z-n^2}|\le \frac{1}{n^2}$ . (Edited)
