Hou would you prove the following?
Let $f(z)=\sum_{n=-\infty}^{\infty}\frac{1}{(n-z)^2}$. Show that it converges on compact subsets of $\mathbb{C} \setminus{\mathbb{Z}}$.
2026-03-29 20:09:43.1774814983
prove series converge on compact sets of $\mathbb{C} \setminus{\mathbb{Z}}$ converge.
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Hint: Let be $K\subset\mathbb{C}\setminus{\mathbb{Z}}$ compact. Take $d_K = \inf{\{|x - y|:\,x\in K, y\in{\mathbb{Z}}\}}$. Prove that $d_K > 0$. Use this and that $K$ is bounded to bound $\frac1{(n - z)^2}$.