The interval of convergence of the series is
Answer to Problem 49E
The interval of convergence and the series converges absolutely as
Explanation of Solution
Given information:
The given series is
Formula used:
The ratio test is used.
Calculation:
The series of absolute values is
The ratio Test let
Then, the series converges if L < I, the series diverges if L >1 and the test is inconclusive if L=1
Using the ratio test, we check for absolute convergence as follows,
The series converges absolutely for
And diverges for
And when
This diverges by the p-test with
And when
This does not converge absolutely, but it converges conditionally by the alternating Series Test.
(a) Interval of convergence:
(b) Series converges absolutely on
(c) Series converges conditionally at
Conclusion:
The interval of convergence and the series converges absolutely as
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus & Its Applications (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd 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