Comparing Series: Convergence or Divergence?

rcmango
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Homework Statement



is the series convergent or divergent.
Sum from 2 to ∞ of 1/ [n(ln n)^.5]

Homework Equations



comparison test?

The Attempt at a Solution



Is it possible to use the comparison test for this problem. Also, could I compare this with something like: (1/[(ln n)^.5] that is very similiar, please help me choose what i need to compare it with.

thankyou.
 
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The integral test seems appropriate for this one. Do you see why?
 

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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