I'm having trouble evaluating this limit:
$ \lim_{x\to\infty} \sum_{n=1}^\infty \frac{x^n}{(n+a)} $
My intuition and initial attempts at making sense of it say that it diverges, and so do a few of my friends, but WolframAlpha says it equals $-\frac{1}{a}$ (if you plug in some values for $a$) and the intermediate steps for those are pretty useless.
For reference: WolframAlpha's evaluation
Can anyone at least point me in the right direction on how to evaluate this limit?
Thanks in advance!