Absolute Convergence: Complex Homework Equations and Solutions

Ted123
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Homework Statement



[PLAIN]http://img225.imageshack.us/img225/7501/complexh.jpg

Homework Equations





The Attempt at a Solution



How do I show this absolutely converges?
 
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What have you tried? It is difficult to help you without seeing what you have done.

What about the ratio test? After simplifying the limit in the ratio test, you'll find that the answer becomes evident. Let us know if you need more guidance than this.

When in doubt, try the ratio test! It's relatively straightforward compared to some of the other tests for convergence.
 

Thread 'Finding the nth roots of a complex number'

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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