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I Summation Equality

  1. Feb 7, 2017 #1
    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!
  2. jcsd
  3. Feb 7, 2017 #2
    Seems fine to me. Have you tried expanding the square or anything?
  4. Feb 7, 2017 #3
    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!
  5. Feb 7, 2017 #4


    Staff: Mentor


    Good suggestion.
  6. Feb 7, 2017 #5

    Stephen Tashi

    User Avatar
    Science Advisor

    Keep in mind that for a constant term ##k## , ##\sum_{k=1}^N k = Nk##.
  7. Feb 8, 2017 #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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