2(-1)r (a + 2)n n2n n=1
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
Determine the radius of convergence and the interval of convergence for each power series.
![The image displays a mathematical expression for an infinite series. It is labeled as item number 9 and is expressed using summation notation. The series is written as:
\[
\sum_{n=1}^{\infty} (-1)^n \frac{(x+2)^n}{n \cdot 2^n}
\]
In this expression:
- The summation symbol \(\sum\) indicates that the terms following it are to be summed from \(n = 1\) to infinity.
- The term \((-1)^n\) introduces alternating signs based on the parity of \(n\).
- The expression \((x+2)^n\) is an exponential term where \(x+2\) is raised to the power of \(n\).
- The denominator \(n \cdot 2^n\) involves \(n\) multiplied by \(2\) raised to the power of \(n\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41847e25-11eb-4a46-b15a-a716d47a2bff%2Fe01d80ec-b4e4-4426-b688-2f560a837f0d%2Fm77ksts_processed.png&w=3840&q=75)
Transcribed Image Text:The image displays a mathematical expression for an infinite series. It is labeled as item number 9 and is expressed using summation notation. The series is written as:
\[
\sum_{n=1}^{\infty} (-1)^n \frac{(x+2)^n}{n \cdot 2^n}
\]
In this expression:
- The summation symbol \(\sum\) indicates that the terms following it are to be summed from \(n = 1\) to infinity.
- The term \((-1)^n\) introduces alternating signs based on the parity of \(n\).
- The expression \((x+2)^n\) is an exponential term where \(x+2\) is raised to the power of \(n\).
- The denominator \(n \cdot 2^n\) involves \(n\) multiplied by \(2\) raised to the power of \(n\).
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