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Summations: Where did this come from

  1. Feb 12, 2010 #1
    Hey can anyone explain to me how the summation 1/(n^2-m^2) = 1/2n[1/(m+n)-1/(m-n)]?

    I am trying to find the second order correction to the energy of a harmonic oscillator (nondegenerate perturbations), and understand everything but where that came from. Is there a table of summation identities online somewhere?
     
  2. jcsd
  3. Feb 12, 2010 #2

    Fredrik

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    [tex]\frac{1}{2n}\left(\frac{1}{m+n}-\frac{1}{m-n}\right)=\frac{1}{2n}\left(\frac{m-n}{(m+n)(m-n)}-\frac{m+n}{(m+n)(m-n)}\right)[/tex]
     
  4. Feb 12, 2010 #3
    Thank you very much! I figured it was something that wasn't a big deal, but sometimes when I'm working on the tougher stuff my brain doesn't want to switch to a lower gear!
     
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