(adsbygoogle = window.adsbygoogle || []).push({}); 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 anywhereonthe radius of convergence.

2. Relevant equations

As an example:

Σ(z+3)^{k2}

with k going from 0 → ∞ andza 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 convergesonthe 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, sayz=-2 orz=-3+iin this case, but I'm not sure what the result would mean.

Thanks for any help you can provide!

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# Complex Power Series Convergence Help!

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