Suppose that h0,h1,h2,... is a sequence dened as follows:

Chapter 5, Problem 5.173

(choose chapter or problem)

Suppose that h0,h1,h2,... is a sequence dened as follows: h0 =1, h1 =2, h2 =3, hk =hk1 +hk2 +hk3 for all integers k 3. a. Prove that hn 3n for all integers n 0. b. Suppose that s is any real number such that s3 s2 +s+1. (This implies that s > 1.83.) Prove that hn sn for all n 2.

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