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1. Let x₁ = k> 0 and 2n+1 = √4xn-1 for all n E J. (a) Determine for what values of k the sequence (zn) (b) For those values of k, prove that the sequence {n} will be monotone increasing. converges, and find its limit.

1. Let x₁ = k> 0 and 2n+1 = √4xn-1 for all n E J. (a) Determine for what values of k the sequence (zn) (b) For those values of k, prove that the sequence {n} will be monotone increasing. converges, and find its limit.

Advanced Engineering Mathematics
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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1. Let 2₁ k> 0 and n+1 = √4,- 1 for all n € J. (a) Determine for what values of k the sequence {n} will be monotone increasing. (b) For those values of k, prove that the sequence {n}1 converges, and find its limit.
Transcribed Image Text:1. Let 2₁ k> 0 and n+1 = √4,- 1 for all n € J. (a) Determine for what values of k the sequence {n} will be monotone increasing. (b) For those values of k, prove that the sequence {n}1 converges, and find its limit.
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