Prove the series $\sum_{n\geq1} \frac{1}{1+z^n}$ is convengent if $|z|>1$. Consider $$\sum_{n\geq1} \frac{1}{1+z^n}$$ with $z\in\mathbb{C}$; I have prove that series is NOT convergent when $|z|\leq1$ to it I applied Weierstrass' method. But I do not know how I can prove that series is convergent when $|z|>1$, someone could help?, thanks

Hint when denominator becomes more than 1 the total mod will become less than 1 so we can prove that the given number is perfect fraction and we are done with the proof.
