This is impossible to answer, as it depends on the value of w, and in fact there is no definite answer for certain values of w. If w = 0 or 2 or 4 etc. the series adds to . If it's anything else the series does not converge, although it is bounded.

selanakf: are you sure you wrote the correct expression:

sum of cos(wt) for t = 1 to infinity?

Please explain how this is equal to 0.