Test the series below for convergence using the Root Test. Σ n=1 5n 8n + 2 n The limit of the root test simplifies to lim f(n)| where 818 f(n) = = The limit is: (enter oo for infinity if needed) Based on this, the series O Converges O Diverges
Test the series below for convergence using the Root Test. Σ n=1 5n 8n + 2 n The limit of the root test simplifies to lim f(n)| where 818 f(n) = = The limit is: (enter oo for infinity if needed) Based on this, the series O Converges O Diverges
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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![**Root Test for Convergence**
**Task:** Test the series below for convergence using the Root Test.
\[
\sum_{n=1}^{\infty} \left( \frac{5n}{8n + 2} \right)^n
\]
**Instructions:**
The limit of the root test simplifies to
\[
\lim_{{n \to \infty}} |f(n)|
\]
where
\( f(n) = \) [Insert your expression here]
The limit is: [Enter limit here] (enter ∞ for infinity if needed)
**Questions:**
Based on this, the series
- [ ] Converges
- [ ] Diverges](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54cb8c7a-f5c8-4f70-beb9-4c302d85da57%2F62f0b3b7-0d36-48dc-8883-b4b33550f25f%2Fttc1wlk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Root Test for Convergence**
**Task:** Test the series below for convergence using the Root Test.
\[
\sum_{n=1}^{\infty} \left( \frac{5n}{8n + 2} \right)^n
\]
**Instructions:**
The limit of the root test simplifies to
\[
\lim_{{n \to \infty}} |f(n)|
\]
where
\( f(n) = \) [Insert your expression here]
The limit is: [Enter limit here] (enter ∞ for infinity if needed)
**Questions:**
Based on this, the series
- [ ] Converges
- [ ] Diverges
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