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Math Help - Proof of equality of finite sum, and trigonometric rational function

  1. #1
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    Proof of equality of finite sum, and trigonometric rational function

    First of all I'm not sure if this is the right place to post this question. It's for a partial differential equations course, but it doesn't seem to have anything to do with differential equations directly.
    I need to prove that 1 + 2 * Sum(n=1,N)(cos(nx)) = sin((N + (1/2))x)/sin((1/2)x).

    I have no idea where to start, other than that we are studying Fourier series. Can someone please help me figure out how to get started?
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  2. #2
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    <br />
S=e^{ia}+e^{i2a}+...+e^{ina}=\frac {e^{i(n+1)a}-1}{e^{ia}-1}<br />
    Your sum is Re(S).
    Last edited by zzzoak; September 30th 2010 at 03:05 PM.
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