What Is the Correct Numerator for Summation with Variable X Sub k?

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I have a problem with an inequality. In the numberator of one term I have X sub k, and in the denominator I have the sum X sub ks from 1 to n. So let's say I use n=2 and have two terms in the denominator Xsub1 and Xsub2. What am I using for the X sub k in the numerator. It definitely is not X sub n.
 
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The k in the numerator does and can not have anything to do with the k in the denominator, unless I'm missing something.
 
The same that I am missing I think. There has to be another summation for that k to exist in the numerator right?
 
barksdalemc said:
The same that I am missing I think. There has to be another summation for that k to exist in the numerator right?

Could you present the problem perhaps..?
 
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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