Summation with exponential functions

  • Thread starter Belgium 12
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  • #1
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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.
 

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  • #2
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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.
 
  • #3
HallsofIvy
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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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