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Sum of a finite sine series

  1. Oct 28, 2008 #1
    Can anyone tell me what is the sum of a finite series of Sines.

    [tex]\sum_{n=1}^N \sin^2 (n \phi) [/tex]. I am going through a text and it gives it as (N+1)/2. I tried to derive it. The N comes out ok when you use the half angle identity but I can't figure out a general rule for the Cosines that appear
  2. jcsd
  3. Oct 29, 2008 #2


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    What is [itex]\phi[/itex]?
  4. Oct 29, 2008 #3
    [tex] \phi = \pi s /(N+1) [/tex] where s = 1,2...N
  5. Oct 29, 2008 #4
    resolve sin^2 into 1-cos something. Put it in terms of complex exponentials. you'll get a geometric series.
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