Summation Equality

  • #1

Main Question or Discussion Point

I'm doing my first paper review and an equation is holding me up. I can't tell if I'm just missing something silly or if the author made a mistake.

Given that:
[tex]\sum_{n=1}^{N}s_{n} = 1[/tex]
The author says that:
[tex]\sum_{n=1}^{N}(s_{n} - \frac{1}{N})^{2} = \sum_{n=1}^{N}s_{n}^{2} - \frac{1}{N}[/tex]
I seem to be having some trouble getting this to work. Am I just missing something? Or is this the author's mistake? Thanks!
 

Answers and Replies

  • #2
70
34
I seem to be having some trouble getting this to work.
Seems fine to me. Have you tried expanding the square or anything?
 
  • #3
Seems fine to me. Have you tried expanding the square or anything?
I did, but still didn't seem to get it to come out right. But, now that I know it's just me, I'll figure it out. Thanks!
 
  • #4
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  • #5
Stephen Tashi
Science Advisor
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I did, but still didn't seem to get it to come out right. But, now that I know it's just me, I'll figure it out. Thanks!
Keep in mind that for a constant term ##k## , ##\sum_{k=1}^N k = Nk##.
 
  • #6
Sorry, I discovered my error very shortly after reading Dragon27's reply. I had made a very simple mistake where I wrote [tex]\frac{N}{N^2}=N[/tex]. Just not enough sleep I guess.
 

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