Question: Suppose that b 0 , b 1 , b 2 , . . . is a sequence defined as follows: b 0 =1, b 1

Suppose that b0, b1, b2, . . . is a sequence defined as follows:

b0 =1, b1 =2, b2 =3, and bk = bk1 + 4*bk2 + 5*bk3 for all integers k 3.

Prove by mathematical induction that bn 3n for all integers n 0.

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