Limit Process Summation Confusion

Whalstib
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Hi,

I have been staring at this for a while. I under stand the process and can account for and reproduce every step of this problem EXCEPT I can nit figure out where the 6i/n coms from. I have included the equation and the issue is highlighted in yellow.

Please explain... this is the last piece of the puzzle.

Thanks,

Warren
 

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uuuuhm, (a+b)^2=a^2+2ab+b^2?
 
Man! I am actually getting the calculus but completely blowing the algebra!

Thanks...sigh...

Warren
 
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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