2. (Series) We will need series to compute probabilities and expectations related to discrete quantities. (a) Assuming r # 1, derive a simple expression for 3,. := 2s (1) i=m as a function of r, m and n, and prove that it holds. Assume m and n are positive integers with m g n. (b) Under what condition on 1' does the innite series 31% Sn (2) 3:17} converge (where again m is a positive integer)? 1 (c) Use induction to prove the identity where n is a nonnegative integer greater than 1