Can Gauss Test Be Applied to Multiple Series?

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Can Gauss test be applied to second and third series. I am totally confused which test to apply on the first series.
 

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For number 3, use Cauchy's test and remember that

\displaystyle \lim_{n\to \infty} \left( 1+\frac{1}{n}\right )^n=e

It will also work nicely for the first problem
 
Thank you Gregg!
 

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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