I have a problem set that asks me to determine, first, the radius of convergence of a complex series (using the limit of the coefficients), and second, whether or not the series converges anywhere on the radius of convergence.
As an example:
with k going from 0 → ∞ and z a complex number
The Attempt at a Solution
I can figure out the radius of convergence easily enough (I think); it would be 1 here, right? My question is just about how to determine whether or not it converges on the circle of convergence. Honestly, I'm not even sure of how to test for convergence at a specific point.
My one thought was to plug in points on the circle, say z=-2 or z=-3+i in this case, but I'm not sure what the result would mean.
Thanks for any help you can provide!