5. Let the sequence (xn) be recursively defined by x1 > 0 and xn+1 = (2+xn)¯¹, n ≥1. Show that (n) is a convergent sequence and evaluate its limit.

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 28E
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5. Let the sequence (xn) be recursively defined by x1 > 0 and
xn+1 =
(2+xn)¯¹, n ≥1.
Show that (n) is a convergent sequence and evaluate its limit.
Transcribed Image Text:5. Let the sequence (xn) be recursively defined by x1 > 0 and xn+1 = (2+xn)¯¹, n ≥1. Show that (n) is a convergent sequence and evaluate its limit.
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