Simple Manipultion - what am I missing?

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meb09JW
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Hi,

I'm not sure how to go from the top-right to the bottom left.

It seems like they have differentiated the top and bottom separately... but I think there is some e identity I have forgotten?

thanks!
 

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It looks like that for k=0 they use l'hopital's rule, because when k=0 you have 0/0 (but maybe this is not the limit). I don't know what is k,N,j, etc.
 
Looks kind of sketchy to me. When k=0, they're dividing by zero, so you can't really say the sum is equal to that quotient. It's better if you go back and look at the original series for the k=0 case.
 

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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