## Sum of Cosines

1. The problem statement, all variables and given/known data
I try to simplify to get rid of sum
$$\sum_{k=0}^{n-1}cos(2 \pi fk)$$

2. Relevant equations

3. The attempt at a solution

I discover I shall use euler equation to form:

$$\sum_{k=0}^{n-1}\frac{1}{2}(e^{2 \pi fki}+e^{-2 \pi fki})$$

but how to sum exponentials?
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 Recognitions: Gold Member Homework Help Science Advisor Staff Emeritus Aren't those geometric series?
 but do I include exp() when I do geometric series?

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## Sum of Cosines

You need to express the terms in the form Ark. Use whatever A and r allow you to do this.
 is it $$\frac{1-exp(2 \pi fi)^{t}}{1-exp(2 \pi fi)}$$
 Recognitions: Gold Member Homework Help Science Advisor Staff Emeritus If by t you mean n, that would be twice the sum of the first term. You might find it a little simpler to start with cos x = Re[eix]. Then you only have one term to deal with and no 1/2's floating around.
 thank you very much!!

 Tags cosine, euler, exponentials, series, sum