Analytic continuation of $\sum (z/a)^n$ I'm having trouble continuing this function beyond its convergence radius, $R=a$.
$$f(z)=\sum (z/a)^n$$
Given the context (a textbook in complex analysis) I suspect it should have a simple closed-form expression. I've tried differentiating and trying to relate it to the geomtric series, but so far I haven't had any success.
Any hint or idea on how to analytic continuate it?
Thanks in advance!

For $|z/a|<1$ the sum is $\frac{1}{1-(z/a)} = \frac{a}{a-z}$. That is the continuation. 
