Test for convergence of a series

Michael_Light
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Homework Statement



Mathematics 11.png


Homework Equations





The Attempt at a Solution



I have no ideas how to continue. I also tried the comparison test but I don't know where to start. Please guide me...
 
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You want the limit of the ratio as n->infinity. Look at just the \frac{(n+1)^k}{n^k} part. That's the same as (\frac{n+1}{n})^k=(1+\frac{1}{n})^k. What is that limit?
 

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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