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## Homework Statement

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.

## Homework Equations

As an example:

Σ(

*z*+3)

^{k2}

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!

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