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

• Sep 30th 2010, 01:11 PM
nivekious
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?
• Sep 30th 2010, 01:49 PM
zzzoak
$
S=e^{ia}+e^{i2a}+...+e^{ina}=\frac {e^{i(n+1)a}-1}{e^{ia}-1}
$