Test the series below for convergence using the Ratio Test. n + 1 53n +3 n=1 The limit of the ratio test simplifies to lim |f(n)| where f(n) = The limit is: (enter oo for infinity if needed) Based on this, the series Select an answer ♥
Test the series below for convergence using the Ratio Test. n + 1 53n +3 n=1 The limit of the ratio test simplifies to lim |f(n)| where f(n) = The limit is: (enter oo for infinity if needed) Based on this, the series Select an answer ♥
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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![## Testing Series Convergence Using the Ratio Test
Consider the series:
\[
\sum_{n=1}^{\infty} \frac{n + 1}{5^{3n+3}}
\]
### Applying the Ratio Test
To determine the convergence of this series, we simplify the limit of the ratio test to:
\[
\lim_{n \to \infty} |f(n)|
\]
where
\[
f(n) = \text{(Enter the expression here)}
\]
Calculate the limit:
\[
\text{The limit is: }\quad \text{(Enter oo for infinity if needed)}
\]
### Conclusion
Based on this, the series:
\[
\text{Select an answer: (Converges / Diverges)}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc247148b-ac88-4d23-ab16-d846cf9acaa7%2Fc093d23b-4a68-4e93-93b3-4036684e1f39%2F7efewbh_processed.png&w=3840&q=75)
Transcribed Image Text:## Testing Series Convergence Using the Ratio Test
Consider the series:
\[
\sum_{n=1}^{\infty} \frac{n + 1}{5^{3n+3}}
\]
### Applying the Ratio Test
To determine the convergence of this series, we simplify the limit of the ratio test to:
\[
\lim_{n \to \infty} |f(n)|
\]
where
\[
f(n) = \text{(Enter the expression here)}
\]
Calculate the limit:
\[
\text{The limit is: }\quad \text{(Enter oo for infinity if needed)}
\]
### Conclusion
Based on this, the series:
\[
\text{Select an answer: (Converges / Diverges)}
\]
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