Summations: Where did this come from

[karenmarie3]

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?

 

[Fredrik]

$$\frac{1}{2n}\left(\frac{1}{m+n}-\frac{1}{m-n}\right)=\frac{1}{2n}\left(\frac{m-n}{(m+n)(m-n)}-\frac{m+n}{(m+n)(m-n)}\right)$$

 

[karenmarie3]

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!