Find a closed formula for...

Find a formula for:
1+cos(x)+cos(2x)+ ... + cos(nx)

Any help?

cos(x) = (exp(ix) + exp(-ix)) / 2

=> sum cos(kx) (k=0->n)

= sum (1/2) exp(ikx)

+ sum (1/2) exp(-ikx)

(k=0->n)

= (1/2) ((1 - exp(i(k+1)x))/(1 - exp(ix)) + (1 - exp(-i(k+1)x))/(1 - exp(-ix)))

(geometric series)