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(1) A sequence an is given by a₁ = √2, an+1 = √2+ an. (a) By induction or otherwise, show that an is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that exists. (b) Find liman-

(1) A sequence an is given by a₁ = √2, an+1 = √2+ an. (a) By induction or otherwise, show that an is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that exists. (b) Find liman-

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) A sequence an is given by a₁ = √√2, an+1 = √2+ an. (a) By induction or otherwise, show that an is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that exists. (b) Find limno an (2) Logarithmic p-series (a) Show that the improper integral dx ₁7(In 2)P (p a positive constant) converges if and only if p > 1. (b) What implications does the fact in part (a) have for the convergence of the series 1 n(ln n)P Give reasons for your answer. n=2 -?
Transcribed Image Text:(1) A sequence an is given by a₁ = √√2, an+1 = √2+ an. (a) By induction or otherwise, show that an is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that exists. (b) Find limno an (2) Logarithmic p-series (a) Show that the improper integral dx ₁7(In 2)P (p a positive constant) converges if and only if p > 1. (b) What implications does the fact in part (a) have for the convergence of the series 1 n(ln n)P Give reasons for your answer. n=2 -?
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