Why does 1/[n log(n)]^1.1 converge

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Homework Statement


Prove that the series:
1/[n log(n)]^1.1 converges

Homework Equations




The Attempt at a Solution




We know that nlogn is equal to d[log(log(n))] and use the integral test to show that it diverges.
However, I have no idea how to deal with the 1.1th power.
 
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n > 10

log(n) >1

Thus,

1/[(nlog(n))^(1.1)] < 1/ (n^1.1)
 

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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