Series Ratio Test: Answer 1/7 - Confirm?

naspek
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Hey there.. I've done the ration test for the series at the attachment..
i've got the answer 1/7 where the series is convergent..
can someone confirm my answer..?
 

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Yes, the ratio test gives a ratio of 1/7, so the series converges.
 
Thanks Mark44! =)
 

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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