(a)
The radius of convergence of series
(a)
Answer to Problem 9RE
The radius of convergence for is
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
Check for absolute convergence using ratio test.
Hence,
Therefore,
That gives
Checking convergence at end points At
Since, from equation (1)
Conclusion:
The radius of convergence for is
(b)
The interval of convergence is
(b)
Answer to Problem 9RE
The series always converges for interval
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
Since,
From equation (1) and (2) as shown below,
Therefore,
The series always converges for interval
Conclusion:
The series always converges for interval
(c)
The series
(c)
Answer to Problem 9RE
The series always converges for interval
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
Since,
From equation (1) as shown below,
Therefore,
The series always converges for interval
Conclusion:
The series always converges for interval
(d)
The series
(d)
Answer to Problem 9RE
The rearrangement of the terms affects the convergence of the series.
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
The point of conditional convergence is at x = -1 . Since, the rearrangement of the terms affects the convergence of the series.
Conclusion:
The rearrangement of the terms affects the convergence of the series.
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
University Calculus: Early Transcendentals (4th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Precalculus (10th Edition)
Calculus & Its Applications (14th 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