can you please show step by step on how to solve this especilaly the induction step so i can understand how to approach similaar problems later on please? Let the sequence (xn) be recursively defined by x1 = √2 andxn+1 = √√2+xn, n ≥ 1.Show that (xn) converges and evaluate its limit.

The objective of this question is to prove that the given sequence (xn) converges and to find its…

Answered: Let the sequence (xn) be recursively…

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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can you please show step by step on how to solve this especilaly the induction step so i can understand how to approach similaar problems later on please?

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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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.