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5 a) Let the sequence {an}=1 is defined by a₁ = 4 and an+1 =; for n E N 6-an i. Prove that {an}=1 is a decresing sequence. ii. Prove that 0 < an for all n E N. iii. Find lim an. 12-00 iv. Describe the behaviour of the sequence {an}n=1, if a₁ = 1.

5 a) Let the sequence {an}=1 is defined by a₁ = 4 and an+1 =; for n E N 6-an i. Prove that {an}=1 is a decresing sequence. ii. Prove that 0 < an for all n E N. iii. Find lim an. 12-00 iv. Describe the behaviour of the sequence {an}n=1, if a₁ = 1.

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) Let the sequence {an}n=1 is defined by a, = 4 and an+1 = 5 for n E N 6-an i. Prove that {an}n=1 is a decresing sequence. ii. Prove that 0 < an for all n E N. iii. Find lim an. n-00 iv. Describe the behaviour of the sequence {a,}=1, if a, = 1. b) For each of the following series, determine whether it converges or diverges. justifications and state the name of the convergence test you use. n2" En=1 i. n! n2+2 ii. n%=D1 2n2-п+5.
Transcribed Image Text:a) Let the sequence {an}n=1 is defined by a, = 4 and an+1 = 5 for n E N 6-an i. Prove that {an}n=1 is a decresing sequence. ii. Prove that 0 < an for all n E N. iii. Find lim an. n-00 iv. Describe the behaviour of the sequence {a,}=1, if a, = 1. b) For each of the following series, determine whether it converges or diverges. justifications and state the name of the convergence test you use. n2" En=1 i. n! n2+2 ii. n%=D1 2n2-п+5.
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