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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5f60795-875f-49e4-8e5f-40c9f83025e2%2F9b17c83d-9a4c-45f9-bf61-704fd210c934%2F53d34m_processed.png&w=3840&q=75)
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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