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Sum of Cosines

  1. Jun 11, 2012 #1
    1. The problem statement, all variables and given/known data
    I try to simplify to get rid of sum
    [tex] \sum_{k=0}^{n-1}cos(2 \pi fk)[/tex]

    2. Relevant equations


    3. The attempt at a solution

    I discover I shall use euler equation to form:


    [tex] \sum_{k=0}^{n-1}\frac{1}{2}(e^{2 \pi fki}+e^{-2 \pi fki})[/tex]

    but how to sum exponentials?
     
  2. jcsd
  3. Jun 11, 2012 #2

    vela

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    Aren't those geometric series?
     
  4. Jun 11, 2012 #3
    but do I include exp() when I do geometric series?
     
  5. Jun 11, 2012 #4

    vela

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    You need to express the terms in the form Ark. Use whatever A and r allow you to do this.
     
  6. Jun 11, 2012 #5
    is it [tex]\frac{1-exp(2 \pi fi)^{t}}{1-exp(2 \pi fi)}[/tex]
     
  7. Jun 11, 2012 #6

    vela

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    If by t you mean n, that would be twice the sum of the first term. You might find it a little simpler to start with cos x = Re[eix]. Then you only have one term to deal with and no 1/2's floating around.
     
  8. Jun 11, 2012 #7
    thank you very much!!
     
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