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Consider the sequence a_(n) defined by the recurrence relation a_(n+1) = (-1) ^ ( n) (2n+3)/(3n+2)a_(n) for n > = 1, a _(1) = 1. a) Find the terms a_(2) and a (3). b) Compute the limit lim_(n- > \ infty )|(a_(n+1))/(a_(n))| . c) Does the series [_(n = 1)^(\infty) a_(n) converge or diverge? Explain. d) What is the value of the lim_()itlim_(n-> \infty )a_(n) ? Explain.

Consider the sequence a_(n) defined by the recurrence relation a_(n+1) = (-1) ^ ( n) (2n+3)/(3n+2)a_(n) for n > = 1, a _(1) = 1. a) Find the terms a_(2) and a (3). b) Compute the limit lim_(n- > \ infty )|(a_(n+1))/(a_(n))| . c) Does the series [_(n = 1)^(\infty) a_(n) converge or diverge? Explain. d) What is the value of the lim_()itlim_(n-> \infty )a_(n) ? Explain.

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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Consider the sequence a_(n) defined by the recurrence relation a_(n+1) = (-1) ^ ( n) (2n+3)/(3n+2)a_(n) for n > = 1, a _(1) = 1. a) Find the terms a_(2) and a (3). b) Compute the limit lim_(n- > \ infty )|(a_(n+1))/(a_(n))| . c) Does the series [_(n = 1)^(\infty) a_(n) converge or diverge? Explain. d) What is the value of the lim_()itlim_(n-> \infty )a_(n) ? Explain.
Transcribed Image Text:Consider the sequence a_(n) defined by the recurrence relation a_(n+1) = (-1) ^ ( n) (2n+3)/(3n+2)a_(n) for n > = 1, a _(1) = 1. a) Find the terms a_(2) and a (3). b) Compute the limit lim_(n- > \ infty )|(a_(n+1))/(a_(n))| . c) Does the series [_(n = 1)^(\infty) a_(n) converge or diverge? Explain. d) What is the value of the lim_()itlim_(n-> \infty )a_(n) ? Explain.
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