Determine Convergence or Divergence

Ki-nana18
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Homework Statement


Determine if the series the summation form n=2 to infinity of n/((n2+1)ln(n2+1)) is convergent or divergent.


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The Attempt at a Solution


I applied the integral test and got positive infinity, so I it diverges. But I want to know if I'm right. Am I right?
 
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Right. But you might want to say a few words about why you think the series is valid to treat with the integral test.
 
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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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