Rewriting Power Series - Simple Algebra Question

MillerGenuine
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Homework Statement


My question involves a small algebra issue within a power series problem. I have (-1)^n-1 and i just need to know how i can re-write this. I know that if it were (1)^n+1 i could re-write as (1)^n * (n)
So can i write (-1)^n-1 as (-1)^n * (-1) ?


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The Attempt at a Solution

 
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To answer this, think about what (-1)^{-1} is.
 
(-1)^n-1 = [(-1)^n]/(-1)
 
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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