Integral Test: What should I compare this series with to prove it's convergence?

theBEAST
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Homework Statement


Here is the problem:
http://dl.dropbox.com/u/64325990/HW%20Pictures/integraltest.PNG

The Attempt at a Solution


I know it is convergent because it is very similar to 1/n^1.5 which is convergent as well. However what would I compare this with using the Integral Test to prove that it is convergent?
 
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theBEAST said:

Homework Statement


Here is the problem:
http://dl.dropbox.com/u/64325990/HW%20Pictures/integraltest.PNG

The Attempt at a Solution


I know it is convergent because it is very similar to 1/n^1.5 which is convergent as well. However what would I compare this with using the Integral Test to prove that it is convergent?

Compare it with \frac{\sqrt{2n+2n}}{n^2}. Then it's even more similar to 1/n^(1.5).
 
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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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