I have the two series: C = 1 + (1/3)cosx + (1/9)cos2x + (1/27)cos3x ... (1/3^n)cosnx S = (1/3) sinx + (1/9)sin2x ... (1/3^n)sinnx I have to express, in terms of x, the sum to infinity of these two series. Here's what I've done so far: Let z represent cosx + jsinx C + jS = z^0 + (1/3)Z^1 ... (1/3)^n(Z^n) This is a GP with first term 1, common ratio (1/3)Z. Sum to infinity of C + jS = a/(1-r) = 3/(3-Z) I can't seem to find where to go from there. Can anyone help? Thankyou.