3. Determine whether the follow sequences converge or diverge. If it converges, find the limit. n² a) an Vn³+4n b) an = cos² n 272 c) an=n-√√n +1√n +3
3. Determine whether the follow sequences converge or diverge. If it converges, find the limit. n² a) an Vn³+4n b) an = cos² n 272 c) an=n-√√n +1√n +3
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
Determine whether the follow sequences converge or diverge. If it converges, find the limit.
a) an = N^2/(sqrt(n^3+4n))
b) an = cos^2n/2^n
c) an = n-sqrt(n+1)sqrt(n+3)
![**Problem 3: Convergence and Divergence of Sequences**
Determine whether the following sequences converge or diverge. If it converges, find the limit.
a) \[ a_n = \frac{n^2}{\sqrt{n^2 + 4n}} \]
b) \[ a_n = \frac{\cos^2 n}{2^n} \]
c) \[ a_n = n - \sqrt{n + \sqrt{n + 3}} \]
**Instructions**: Analyze each sequence to determine if it approaches a specific limit as \( n \to \infty \). If no limit exists, describe the nature of the divergence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcad422bc-64ba-4541-be23-0cacc94d0349%2F2e2a70ef-249c-4fb2-8ac7-fe3530ad9056%2F8hn8vxe_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 3: Convergence and Divergence of Sequences**
Determine whether the following sequences converge or diverge. If it converges, find the limit.
a) \[ a_n = \frac{n^2}{\sqrt{n^2 + 4n}} \]
b) \[ a_n = \frac{\cos^2 n}{2^n} \]
c) \[ a_n = n - \sqrt{n + \sqrt{n + 3}} \]
**Instructions**: Analyze each sequence to determine if it approaches a specific limit as \( n \to \infty \). If no limit exists, describe the nature of the divergence.
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