Suppose that ho, h, h is a sequence defined as fol- Iows: ho = 1, h = 2, hy = 3, h = h- +h-+hs for all integers k 2 3. a. Prove that hin < 3" for all integers n2 0. b. Suppose that s is any real number such that 2s+s+1. (This implies that s > 1.83.) Prove that h, Ss for all n 2 2.