Suppose a₁ > a2 > 0. For n ≥ 2, set an+1 (a) {a2k+1} is decreasing and {a2k} is increasing. (b) {n} is convergent. = (an+an-1). Prove that

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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(7) Suppose a₁ > a₂ > 0. For n ≥ 2, set an+1 = 1/(an+an-1). Prove that
a2
(a) {a2k+1} is decreasing and {a2k} is increasing.
(b) [an] is convergent.
Transcribed Image Text:(7) Suppose a₁ > a₂ > 0. For n ≥ 2, set an+1 = 1/(an+an-1). Prove that a2 (a) {a2k+1} is decreasing and {a2k} is increasing. (b) [an] is convergent.
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