(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use cos ( n * x) = (z ^ n + z ^ -n)/2 to express

cos x + cos 3x + cos 5x + ... + cos([2n -1]x)

as a geometric series in terms of z. Hence find this sum in terms of x

2. Relevant equations

3. The attempt at a solution

(z + z^-1)/2 + (z^3 + z^-3)/2 + ... + (z^2n-1 + z-(2n-1))

I want to use the sum of a geometric series, but I can't work out what the common ratio of the terms is. If someone could point me in the right direction it would be greatly appreciated. Thank you very much in advance for you your help.

Benjy

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# Homework Help: Sum of Complex geometric series

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