For what values of x does the series below converge? What is its sum? What series do you get if you differentiate the given series term by term? For what values of x does the new series converge? What is its sum? 1 1 n 1 (x- 3) + (x-3)2- (x – 3)" + ... 1- +... +
For what values of x does the series below converge? What is its sum? What series do you get if you differentiate the given series term by term? For what values of x does the new series converge? What is its sum? 1 1 n 1 (x- 3) + (x-3)2- (x – 3)" + ... 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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![For what values of \( x \) does the series below converge? What is its sum? What series do you get if you differentiate the given series term by term? For what values of \( x \) does the new series converge? What is its sum?
\[ 1 - \frac{1}{2}(x-3) + \frac{1}{4}(x-3)^2 + \cdots + \left( -\frac{1}{2} \right)^n (x-3)^n + \cdots \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c9159da-a431-4a35-8439-34e918757ee3%2F82cae1a2-fb9f-42b2-96e1-ccecd1bfeb9c%2F9w76q5v_processed.png&w=3840&q=75)
Transcribed Image Text:For what values of \( x \) does the series below converge? What is its sum? What series do you get if you differentiate the given series term by term? For what values of \( x \) does the new series converge? What is its sum?
\[ 1 - \frac{1}{2}(x-3) + \frac{1}{4}(x-3)^2 + \cdots + \left( -\frac{1}{2} \right)^n (x-3)^n + \cdots \]
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