Thanks for answering, but I don't see how you got your answer for S-S/4.
Shouldn't the numerators in S/4 be increasing, not just be 1^2? When I subtract S - S/4, I get 1/4 + 1/16 + 1/64 ... so the numerators are always 1. Am I missing something?
Numerators remain the same, only denominators are multiplied by 4. Our goal was to bring the sum into a form that has i instead of in the numerator. We achieved this by using the identity = (a+b)(a-b).