Odd cosn problem

  • Thread starter xuying1209
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  • #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??
 

Answers and Replies

  • #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.
 
  • #3
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Ahh that it was... almost racked my brains out 'cause "π" I read as n ( not [itex]\pi[/itex]) ...
:smile:
 
  • #4
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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:
  • #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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