I need some help with this. I have to show that the follwing series converges compat.
$$\sum_{n=1}^\infty f_n :D:= \{z \in \mathbb{C} | Re(z) > 0 \} \to \mathbb{C}, f_n (z):=\frac{1}{z+n^2} $$
I tried to separate $Re$ and $Im$ to apply the Leibniz-test but $Re$ does not converge to $0$. Can someone give me a hint or which rule to apply or a direction to proceed?