Series Convergence: Can I Create a p-Series?

Dissonance in E
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Homework Statement



infinity
SIGMA sqrt(n) / ((n^2)(ln(n))
n = 2

Homework Equations





The Attempt at a Solution



Could i beat this into a p-series perhaps?
 
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Dissonance in E said:

Homework Statement



infinity
SIGMA sqrt(n) / ((n^2)(ln(n))
n = 2

Homework Equations





The Attempt at a Solution



Could i beat this into a p-series perhaps?
You can't "beat" it into a p-series, but you can compare it to a convergent p-series.
 
Ah I see, thank you.
 
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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