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Odd cosn problem

  1. Mar 28, 2007 #1
    if n is an odd, cosπ/n+cos3π/n+cos5π/n+.....+cos(2n-1)π/n is equal to what????
    And how can I prove it??
     
  2. jcsd
  3. Mar 28, 2007 #2

    HallsofIvy

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    For n= 1, cos(pi/1)= -1.

    For n> 1, n odd, essentially you are adding the real parts of the 2nth roots of unity. Since those roots are symmetric about the imaginary axis, the sum is 0.
     
  4. Mar 28, 2007 #3
    Ahh that it was... almost racked my brains out 'cause "π" I read as n ( not [itex]\pi[/itex]) ...
    :smile:
     
  5. Mar 28, 2007 #4
    I am not sure what is being asked. Is this [tex]\sum cos(n_i)/n_i, or \sum cos(pi*n_i/n_i), or what?[/tex]
     
    Last edited: Mar 28, 2007
  6. Mar 28, 2007 #5

    HallsofIvy

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    I interpreted as sum of [itex] cos(i\pi/n)[/tex] for i= 1 to n-1.
     
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