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(a) A sequence of nonnegative real numbers (an) is defined recursively by 1, 2a An+1 = 3 aj = 0. 3 (i) Using induction, or otherwise, show that (a,) is bounded above by . (ii) Show that (an) is increasing. (iii) Deduce that (an) converges, and find its limit, justifying any assertions that you make.

(a) A sequence of nonnegative real numbers (an) is defined recursively by 1, 2a An+1 = 3 aj = 0. 3 (i) Using induction, or otherwise, show that (a,) is bounded above by . (ii) Show that (an) is increasing. (iii) Deduce that (an) converges, and find its limit, justifying any assertions that you make.

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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(a) A sequence of nonnegative real numbers (an) is defined recursively by 1. 2a, An+1 = 3 a = 0. 3 (i) Using induction, or otherwise, show that (an) is bounded above by . (ii) Show that (an) is increasing. (iii) Deduce that (an) converges, and find its limit, justifying any assertions that you make.
Transcribed Image Text:(a) A sequence of nonnegative real numbers (an) is defined recursively by 1. 2a, An+1 = 3 a = 0. 3 (i) Using induction, or otherwise, show that (an) is bounded above by . (ii) Show that (an) is increasing. (iii) Deduce that (an) converges, and find its limit, justifying any assertions that you make.
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