Problem

Suppose that h0, h1, h2, ... is a sequence defined as follows:h0 = 1, h1 = 2, h2 = 3,hk =...

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 hnsn for all n ≥ 2.

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Solutions For Problems in Chapter 5.4