separated list of values.) (3x)" (2n)! n-0
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
![**Finding the Interval of Convergence for a Power Series**
### Task:
Find the interval of convergence of the power series. Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma-separated list of values.
### Power Series:
\[
\sum_{{n=0}}^{\infty} \frac{{(2x)^n}}{{(2n)!}}
\]
### Explanation:
To determine the interval of convergence, apply the ratio test or the root test, and check for convergence at the endpoints.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15d21cd-3875-4270-92b4-6749e1bc7456%2Fb4834ffe-71b7-41a3-b001-eebd143a681d%2Frd86g6l_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Interval of Convergence for a Power Series**
### Task:
Find the interval of convergence of the power series. Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma-separated list of values.
### Power Series:
\[
\sum_{{n=0}}^{\infty} \frac{{(2x)^n}}{{(2n)!}}
\]
### Explanation:
To determine the interval of convergence, apply the ratio test or the root test, and check for convergence at the endpoints.
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