Find the radius of convergence, R, of the following series. 00 2 n!(9x - 1)" R =
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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![**Problem Statement:**
Find the radius of convergence, \( R \), of the following series:
\[
\sum_{n=1}^{\infty} n!(9x - 1)^n
\]
\( R = \) [Enter your answer here]
---
**Task:**
Find the interval, \( I \), of convergence of the series.
**Options:**
- \(\bigcirc\) \( I = \left( -\frac{1}{9}, 0 \right) \cup \left\{ \frac{1}{9} \right\}\)
- \(\bigcirc\) \( I = \{ 1 \} \)
- \(\bigcirc\) \( I = \left\{ \frac{1}{9} \right\} \)
- \(\bigcirc\) \( I = \{ 0 \} \)
- \(\bigcirc\) \( I = \left[ -\frac{1}{9}, \frac{1}{9} \right] \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51766312-77d6-4388-ba53-71601d5219eb%2F7645f0ef-2fc7-4c31-b6ab-35b303acdf4c%2Fyyqpl7k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the radius of convergence, \( R \), of the following series:
\[
\sum_{n=1}^{\infty} n!(9x - 1)^n
\]
\( R = \) [Enter your answer here]
---
**Task:**
Find the interval, \( I \), of convergence of the series.
**Options:**
- \(\bigcirc\) \( I = \left( -\frac{1}{9}, 0 \right) \cup \left\{ \frac{1}{9} \right\}\)
- \(\bigcirc\) \( I = \{ 1 \} \)
- \(\bigcirc\) \( I = \left\{ \frac{1}{9} \right\} \)
- \(\bigcirc\) \( I = \{ 0 \} \)
- \(\bigcirc\) \( I = \left[ -\frac{1}{9}, \frac{1}{9} \right] \)
![**Problem Statement:**
Find the radius of convergence, \( R \), of the series.
\[
\sum_{n=1}^{\infty} \frac{(x - 5)^n}{n^n}
\]
**Task 1: Radius of Convergence**
\( R = \underline{\hspace{2cm}} \)
**Task 2: Interval of Convergence**
Find the interval, \( I \), of convergence of the series. (Enter your answer using interval notation.)
\( I = \underline{\hspace{2cm}} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51766312-77d6-4388-ba53-71601d5219eb%2F7645f0ef-2fc7-4c31-b6ab-35b303acdf4c%2Fnqefvhq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the radius of convergence, \( R \), of the series.
\[
\sum_{n=1}^{\infty} \frac{(x - 5)^n}{n^n}
\]
**Task 1: Radius of Convergence**
\( R = \underline{\hspace{2cm}} \)
**Task 2: Interval of Convergence**
Find the interval, \( I \), of convergence of the series. (Enter your answer using interval notation.)
\( I = \underline{\hspace{2cm}} \)
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