Hello. I'd like to show that the series

$\displaystyle \displaystyle \sum_{n=1}^\infty \frac{(-1)^n}{z-n}$

converges uniformly on any domain not containing an integer.

I'm not exactly sure how to handle this. It looks similar to an alternating harmonic series, so I can't use the $\displaystyle M$-test on it.

I would appreciate any suggestions for this problem.