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Odd cosn problem

  1. Mar 28, 2007 #1

    xuying1209

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    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??
     
    xuying1209, Mar 28, 2007
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  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.
     
    HallsofIvy, Mar 28, 2007
  4. Mar 28, 2007 #3

    tehno

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    Ahh that it was... almost racked my brains out 'cause "π" I read as n ( not [itex]\pi[/itex]) ...
    :smile:
     
    tehno, Mar 28, 2007
  5. Mar 28, 2007 #4

    robert Ihnot

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    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
    robert Ihnot, 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.
     
    HallsofIvy, Mar 28, 2007
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