Prove that for every $z \in \mathbb{C}$, the series $\sum_{n=1}^{\infty} \frac{\sin(z/n)}{n}$ converges. For $z \in \mathbb{C}$, let $f(z) = \sum_{n=1}^{\infty} \frac{\sin(z/n)}{n}$. Prove that $f$ is entire.
Prove that for every $z \in \mathbb{C}$, the series $\sum_{n=1}^{\infty} \frac{\sin(z/n)}{n}$ converges. For $z \in \mathbb{C}$, let $f(z) = \sum_{n=1}^{\infty} \frac{\sin(z/n)}{n}$. Prove that $f$ is entire.