Math Help - sum of 1+cos(x)+...+cos(nx)

1. sum of 1+cos(x)+...+cos(nx)

hi
i have little problem here with this problem

i have to find a formula for this sum serie

1+cos(x)+cos(2x)+cos(3x)+....+cos(nx)

the hint is i have to use sum of geometric series with the general term e^(ikX)

thanks

2. there's other way of doing this, or are you really asked to do it by using that hint?

3. i solved it with the hint
thanks any way

4. Originally Posted by livan1
i solved it with the hint
thanks any way
good job. the trick of course was to realize that your sum is the real part of the sum $\sum_{k = 0}^\infty e^{i(kx)}$, which can be interpreted as a geometric series for which you know the formula.

Originally Posted by Krizalid
there's other way of doing this, or are you really asked to do it by using that hint?
just for fun (and curiosity) what other ways were you thinking of, Kriz?