1. The problem statement, all variables and given/known data 2. Relevant equations a(1-r^[n+1])/(1-r) 3. The attempt at a solution So I wrote it as e^(-iNz) [1 + e^(iz) + e^(2iz) + ... + e^(2iNz)] Let r = e^(iz), a=e^(-iNz) a [1 + r + r^2 + ... + r^(2N)] From here I'm not sure what to do. I tried letting n=2N, and then letting the bracket be equal to (1-r)^-1 but I couldn't get much out of that. Tried using the formula, can't get anything. I just get loads of e's everywhere, and no way to get rid of the cos if I put them in trig form. Really stuck.