Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. (If you need to use co or -co, enter INFINITY or -INFINITY, respectively.) (-1)"+ n 1.9. 17 (8n + 1) an+1 =0 lim O converges O diverges Need Heln?
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. (If you need to use co or -co, enter INFINITY or -INFINITY, respectively.) (-1)"+ n 1.9. 17 (8n + 1) an+1 =0 lim O converges O diverges Need Heln?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Text Transcription for Educational Website:**
---
**Topic: Series Convergence Using the Ratio Test**
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
\[ \sum_{n=0}^{\infty} \frac{(-1)^{n+1} n!}{1 \cdot 9 \cdot 17 \cdots (8n+1)} \]
\[
\lim_{{n \to \infty}} \left| \frac{a_{n+1}}{a_n} \right| = 0
\]
- **converges**
- **diverges** ✔
**Need Help?**
- [Read It]
- [Watch It]
**Explanation of Diagram:**
The expression denotes the series and applies the Ratio Test, where the limit of the absolute value of the ratio of consecutive terms is calculated. The student has evaluated the limit as zero, which is marked with a red "X" indicating a mistake in the response, suggesting that this solution should lead to identifying whether the series converges or diverges. The "diverges" option is checked, indicating that the series ultimately diverges.
**Interactive Help Options:**
- **Read It**: Provides written explanations or examples for better understanding.
- **Watch It**: Offers video guidance on solving similar problems.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7da64f87-97a6-4ade-9565-5d171f68500b%2Fb7aa2670-b10e-4251-b357-250d59e840a8%2Fxjwnqet_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Text Transcription for Educational Website:**
---
**Topic: Series Convergence Using the Ratio Test**
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
\[ \sum_{n=0}^{\infty} \frac{(-1)^{n+1} n!}{1 \cdot 9 \cdot 17 \cdots (8n+1)} \]
\[
\lim_{{n \to \infty}} \left| \frac{a_{n+1}}{a_n} \right| = 0
\]
- **converges**
- **diverges** ✔
**Need Help?**
- [Read It]
- [Watch It]
**Explanation of Diagram:**
The expression denotes the series and applies the Ratio Test, where the limit of the absolute value of the ratio of consecutive terms is calculated. The student has evaluated the limit as zero, which is marked with a red "X" indicating a mistake in the response, suggesting that this solution should lead to identifying whether the series converges or diverges. The "diverges" option is checked, indicating that the series ultimately diverges.
**Interactive Help Options:**
- **Read It**: Provides written explanations or examples for better understanding.
- **Watch It**: Offers video guidance on solving similar problems.
---
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