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Summation with exponential functions

  1. Mar 1, 2013 #1
    Dear members,

    see attached pdf file.Can you help me to prove this formulas.

    Thank you

    Belgium 12

    This is not homework.I'm 68 and retired.
     

    Attached Files:

  2. jcsd
  3. Mar 1, 2013 #2
    The terms are a composition of [tex]\left(\frac{1}{z}\right)^k[/tex] and [tex]e^z .[/tex] There should be a nice geometric series formula for this.
     
  4. Mar 1, 2013 #3

    HallsofIvy

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    Staff Emeritus
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    Yes. [itex]e^{kz}= (e^z)^k[/itex] and [itex](-1)^{k-1}e^{kz}= -((-1)e^z)^k[/itex].

    So use the fact that the geometric series [itex]\sum_{k=0}^\infty ar^k[/itex] is [itex]a/(1- r)[/itex].
     
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