1. The problem statement, all variables and given/known data 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. 2. Relevant equations As an example: Σ(z+3)k2 with k going from 0 → ∞ and z a complex number 3. 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!