Series Summation: Does the Ratio Test Determine Convergence or Divergence?

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I have this HW problem: Suppose Un and Vn are sequences of positve numbers such that the ratio of Un+1/Un will always we less than Vn+1/Vn. Show that 1) If Vn converges Un converged and 2) If Un diverges, Vn diverges.

I did the first part by showing that for any n, the ration of Un/Vn is decreasing and if lim of the ratio=M then Un=MVn.

Stuck on the second part.
 
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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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