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
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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.
Transcribed Image Text: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.
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