Complex analysis question (only need a hint)

[fresh]

i know it's supposed to be a simple question. frustrating because it is not coming to me. just want a hint.

question is:
how do you write
1 + cos(theta) + cos (2*theta) + cos(3*theta)... cos(n*theta) using the fact that (z^(n+1) -1) / (z^(n) -1) = 1 + z + z^(2) +... + z^(n)

thanks in advance

 

[dextercioby]

How about
$$Re \sum_{k=0}^{n} e^{ikz}$$

or sum over real of the same "animal"...Which one u prefer...??

Daniel.

PS.Or theta,but it's cusomary to denote complex variables with "z"...

 

[M98Ranger]

Hint: Try using the fact that cos(theta) = (e^(i*theta) + e^(-i*theta)) / 2 and simplify the expression using the given formula.