Proof of a summation=0?

**asq** · September 7th 2010, 07:00 AM

Prove that sum that :

Sum ( i=1 to N) of ( Xi-Xbar)/ N ((X^2)bar - (Xbar)^2) = 0

I know this is something simple like putting everything in terms of Xi/N and cancelling but my brain isn't working today...please help?

**Plato** · September 7th 2010, 07:21 AM

Originally Posted by asq

Prove that sum that : Sum ( i=1 to N) of ( Xi-Xbar)/ N ((X^2)bar - (Xbar)^2) = 0

I have a hard time reading the post But this may help.
$\;\overline X = \dfrac{{\sum\limits_{n = 1}^N {x_n } }}<br /> {N}\, \Rightarrow \,\,\sum\limits_{n = 1}^N {\overline X } = N\overline X = \sum\limits_{n = 1}^N {x_n }$

**asq** · September 8th 2010, 05:15 AM

Yeah, as I said my brain just didn't want to work. I realized that the denominator in that fraction can be factored out (not dependent on i) and then its just very simple to proof that sum Xn-xbar=0.

Thanks!

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