b) Suppose that x₁ > 3 and xn+1 = 2 + √√xn-2 for ne N. If xn → x as n→ ∞, then x = 3. If 20

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Only b and c if possible.
2.2.8. Using the result in Exercise 2.2.5, prove the following results.
a) Suppose that 0 ≤ x1 ≤ 1 and xn+1 = 1-√√1- xn for ne N. If xn → x
2321083X3
as n→∞, then x = 0 or 1.
101 asigna
b) Suppose that x₁ > 3 and xn+1 = 2 + √√xn-2 for ne N. If xn → x as
n→ ∞, then x = 3.
(c)
Suppose that x₁ ≥ 0 and xn+1 √2+xn for ne N. If xnx as
n → ∞, then x = 2. What happens if x₁ > -2?
1
Transcribed Image Text:2.2.8. Using the result in Exercise 2.2.5, prove the following results. a) Suppose that 0 ≤ x1 ≤ 1 and xn+1 = 1-√√1- xn for ne N. If xn → x 2321083X3 as n→∞, then x = 0 or 1. 101 asigna b) Suppose that x₁ > 3 and xn+1 = 2 + √√xn-2 for ne N. If xn → x as n→ ∞, then x = 3. (c) Suppose that x₁ ≥ 0 and xn+1 √2+xn for ne N. If xnx as n → ∞, then x = 2. What happens if x₁ > -2? 1
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