Radius of convergance complex power series

Nikitin
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Homework Statement



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I need help with 7b. Theorem 3 = termwise differentiation and theorem 4 = termwise integration.

Homework Equations


The Attempt at a Solution



I have no idea how differentiation or integration would help me. Can somebody post a short strategy I can use? Please?
 
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Termwise integration gives a term to "cancel" the n in the numerator (not exactly, however). That's not really necessary, but at least it uses integration.
 
Hey! I solved it after looking at the problem with a fresh mind. Thx for the comment, tho
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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