3. Determine whether the series converges or diverges. Show all work and give a clear explanation of your solution. a) Use the Root Test: +00 Σ n-1 (3n-1 5n+1, 2" (n-1)! n! b) Use the Ratio Test ² n-1
3. Determine whether the series converges or diverges. Show all work and give a clear explanation of your solution. a) Use the Root Test: +00 Σ n-1 (3n-1 5n+1, 2" (n-1)! n! b) Use the Ratio Test ² n-1
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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Question
![3. Determine whether the series converges or diverges. Show all work and give a clear explanation of your solution.
a) Use the Root Test:
\[
\sum_{n=1}^{\infty} \left( \frac{3n-1}{5n+1} \right)^n
\]
b) Use the Ratio Test:
\[
\sum_{n=1}^{\infty} \frac{2^n(n-1)!}{n!}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa06fb91f-1445-4bd6-b9dd-268642fc0d22%2Fca03b293-6635-468e-ae5f-9088f3291009%2Fwypxwql_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Determine whether the series converges or diverges. Show all work and give a clear explanation of your solution.
a) Use the Root Test:
\[
\sum_{n=1}^{\infty} \left( \frac{3n-1}{5n+1} \right)^n
\]
b) Use the Ratio Test:
\[
\sum_{n=1}^{\infty} \frac{2^n(n-1)!}{n!}
\]
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