Proofs by Induction Express the following in summation notation. (a) 1 + 20 + 400 + 8, 000, (b) -3 - 1 + 1 + 3 + 5 + 7 Express the following in summation notation and use induction to prove for n (a natural number): 1. 1 + 3 + 5 +...+(2n - 1) = n^2 2. S_1 = 1, S_n = S_n - 1 + 2n for all n greaterthanorequalto 2 Write a recursive algorithm that computes S_n = 2 + 4 + 6 +... +2n Give a proof using mathematical induction that your algorithm is correct