Suppose b1, b2, b3, ... is a sequence defined as follows: b1 = 4, b2 = 12, bk = bk-2 + bk-1 for each integer k≥3. Prove that bn is divisible by 4 for every integer n≥1.

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Description: Suppose b1, b2, b3, ... is a sequence defined as follows: b1 = 4, b2 = 12, bk = bk-2 + bk-1 for each integer k≥3. Prove that bn is divisible by 4 for every integer n≥1.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose b₁, b₂, b₃, ... is a sequence defined as follows:

b₁ = 4, b₂ = 12,

b_k = b_k-2 + b_k-1 for each integer k≥3.

Prove that b_n is divisible by 4 for every integer n≥1.

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