Suppose that g1, g2, g3,... is a sequence defined as follows: g1 = 3, g2 = 5 gk = 3gk1

Chapter 5, Problem 7

(choose chapter or problem)

Suppose that \(g_{1}, g_{2}, g_{3}\), . . . is a sequence defined as follows:

\(g_{1} = 3, g_{2} = 5\)

\(g_{k} = 3g_{k−1} − 2g_{k−2}\) for all integers k ≥ 3.

Prove that \(n = 2^{n} + 1\) for all integers n ≥ 1.

Text Transcription:

g_1, g_2, g_3

g_1 = 3, g_2 = 5

g_k = 3g_k−1 − 2g_k−2

n = 2^n + 1