Prob. 6(d), Chap. 3 in Baby Rudin: Given $z \in \mathbb{C}$, does the series $\sum \frac{1}{1+z^n}$ converge or diverge?
Proving the convergence of $\sum\limits_{n=1}^{\infty}\frac{1}{1+z^n}$ for $|z| > 1$