Theorem 21. The set of x values for which the power series Cn(x – a)" converges can n=0 always be viewed as an interval centered at a. The types of intervals fall into three classes. 1. The interval contains a single point [a, a], and the radius of convergence is 0. 2. The interval is the entire real line. One representation of the real line is (-∞, ), and the radius of convergence is . 3. The interval has a finite positive radius R. There are four possible sub-cases: [a – R, a + R] (a – R, a + R] [a – R, a + R) (a – R, a + R) In(n)x" 2. E n2 n=1
Theorem 21. The set of x values for which the power series Cn(x – a)" converges can n=0 always be viewed as an interval centered at a. The types of intervals fall into three classes. 1. The interval contains a single point [a, a], and the radius of convergence is 0. 2. The interval is the entire real line. One representation of the real line is (-∞, ), and the radius of convergence is . 3. The interval has a finite positive radius R. There are four possible sub-cases: [a – R, a + R] (a – R, a + R] [a – R, a + R) (a – R, a + R) In(n)x" 2. E n2 n=1
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the interval of convergence and the radius of convergence for each series.
![Theorem 21. The set of x values for which the power series Cn(x – a)" converges can
n=0
always be viewed as an interval centered at a. The types of intervals fall into three classes.
1. The interval contains a single point [a, a], and the radius of convergence is 0.
2. The interval is the entire real line. One representation of the real line is (-∞, ), and
the radius of convergence is .
3. The interval has a finite positive radius R. There are four possible sub-cases:
[a – R, a + R]
(a – R, a + R]
[a – R, a + R)
(a – R, a + R)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe407d652-d38b-4cb6-9925-54cb165c137e%2F2580967d-a734-4184-95d6-c444173f8f36%2Fur9d1t.png&w=3840&q=75)
Transcribed Image Text:Theorem 21. The set of x values for which the power series Cn(x – a)" converges can
n=0
always be viewed as an interval centered at a. The types of intervals fall into three classes.
1. The interval contains a single point [a, a], and the radius of convergence is 0.
2. The interval is the entire real line. One representation of the real line is (-∞, ), and
the radius of convergence is .
3. The interval has a finite positive radius R. There are four possible sub-cases:
[a – R, a + R]
(a – R, a + R]
[a – R, a + R)
(a – R, a + R)
Transcribed Image Text:In(n)x"
2. E
n2
n=1
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