Integral for Multiple Natural Logs

Dragon M.
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Homework Statement



I need to find whether or not the Ʃ1/(n(ln n)(ln(ln(n)))) (from 2 to infinity) converges or diverges using the Integral test. I think the best question to ask is where to start with the integral?


Homework Equations



None.


The Attempt at a Solution



I've tried integrating by parts, but I can't find du or v for 1/(lnx)ln(ln(x)). Is there a way to simplify this into a more friendly form?
 
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If you let u= ln(ln(x)) then du= (1/ln(x))(1/x)dx.
 

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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