State where the power series is centered. (-1)*(x – 8π)4n (4n)! ΣΕ Π=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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Please make sure the answers are clear n easy to read. Please do it on white paper. Again make sure the answer is clear. i just need correct answer. do it on white paper
![The image presents a mathematical problem and a corresponding power series for analysis. The task is to determine where the power series is centered.
The series is expressed as follows:
\[
\sum_{n=0}^{\infty} \frac{(-1)^n (x - 8\pi)^{4n}}{(4n)!}
\]
Below the series, there is a blank box provided for the answer.
**Explanation:**
The series given is a power series. A power series takes the form:
\[
\sum_{n=0}^{\infty} a_n (x - c)^n
\]
where \(c\) is the center of the series. In this case, the expression \((x - 8\pi)^{4n}\) indicates that the series is centered at \(x = 8\pi\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63437041-d160-41f3-b7c5-850649685bb2%2F81cf6966-5da7-4278-8b92-0eb2806d3546%2F8o4gabq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents a mathematical problem and a corresponding power series for analysis. The task is to determine where the power series is centered.
The series is expressed as follows:
\[
\sum_{n=0}^{\infty} \frac{(-1)^n (x - 8\pi)^{4n}}{(4n)!}
\]
Below the series, there is a blank box provided for the answer.
**Explanation:**
The series given is a power series. A power series takes the form:
\[
\sum_{n=0}^{\infty} a_n (x - c)^n
\]
where \(c\) is the center of the series. In this case, the expression \((x - 8\pi)^{4n}\) indicates that the series is centered at \(x = 8\pi\).
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