Suppose that h0, h1, h2, ... is a sequence defined as
Chapter 5, Problem 8E(choose chapter or problem)
Problem 8E
Suppose that h0, h1, h2, ... is a sequence defined as follows:
h0 = 1, h1 = 2, h2 = 3,
hk = hk-1 + hk-2+ hk-3 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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