(a) Without the help of the geometric series formula, prove that S1 = Xb n=a rn = ra − rb 1 1 − r , where a, b ∈ Z, a < b, and |r| < 1. Show intermediate steps clearly.
(b) Derive the analytic form of S2 = Xb n=a nrn. The final expression must not contain the summation sign.