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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27ae23ce-e402-42d8-8a45-784eb26c3f7e%2F69342082-bd4e-4ca5-be4d-f0a074cd29d1%2F7ymtxmr_processed.png&w=3840&q=75)
Transcribed Image Text: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.
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