
To calculate: The interval of convergence of the series and an explicit formula for

Answer to Problem 31E
The interval of convergence of the series is
Explanation of Solution
Given information:
There is, its coefficients are
Concept Used:
The infinite sum of the geometric progression is
Calculation:
The series given is
Then function can also be written as
This function is a geometric series with first term
Therefore
This geometric series converges when the value of common ratio
Therefore, the interval of convergence is
Conclusion:
The interval of convergence of the series 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





