2. Let the sequence (xn) be recursively defined by x₁ = √√2 and Xn+1 = √2+xn, n≥1. Show that (xn) converges and evaluate its limit.
2. Let the sequence (xn) be recursively defined by x₁ = √√2 and Xn+1 = √2+xn, n≥1. Show that (xn) converges and evaluate its limit.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 8RE
Question
Let the sequence (n) be recursively defined by x1 = √2 and Xn+1 = √√2+xn, n≥ 1. Show that (n) converges and evaluate its limit. Please be specific during the induction step so i can understand,
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