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Rewritting sum as hyperbolic sine

  1. Oct 24, 2008 #1
    Hi all,

    I have to rewrite a serie into a fraction of hyperbolic sine but I am lost.... My problem looks like this

    [tex]\Sigma_{n=0}^{\infty} exp(K*F)*exp(-F*B(n+0.5))[/tex]

    which can be rearranged into

    [tex] exp(K*F)/(sinh(FB/2) [/tex]

    my problem is I cannot relate the serie


    any hints or advice appreciated.

    Thanks in advance

    1. The problem statement, all variables and given/known data

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    3. The attempt at a solution
  2. jcsd
  3. Oct 24, 2008 #2


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    Homework Helper

    Take the 0.5 part out, so you have e^(FK)*e^(-FB/2)*e^(-FBn). You want the sum over n of e^(-FBn). That's the same as (e^(-FB))^n. It's a geometric series.
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