Does the Integral Test \(\sum_{n=1}^{\infty}\frac{\ln n}{n^p}\) Converge?

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<br /> \sum_{n=1}^{\infty}\frac{lnn}{n^P}<br />
<br /> \int_{1}^{\infty}lnx(x^{-P})dx<br />
 
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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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