To calculate:The radius of convergence and interval of convergence of the series.
Answer to Problem 3E
The Radius of convergence is
Explanation of Solution
Given information:
Concept Used:
Ratio Test:
(i) If
(and therefore convergent)
(ii) If
(iii) If
Calculation:
The series is
Then,
Use of ratio test
By the ratio test, the given series converges if
This means the radius of convergence is
And the series converges in the interval
If
Which converges by alternating series test.
If
Which diverges by Intergral test.
Therefore the given series converges when
So the interval of convergence is
Conclusion:
The Radius of convergence is
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning