(a)
The radius of convergence for the series is
(a)
Answer to Problem 8RE
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.
Therefore, the series is convergence for all real x. Therefore, the radius of convergence for is
Conclusion:
The radius of convergence for is
(b)
The interval of convergence
(b)
Answer to Problem 8RE
The series always converges for interval
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
Since,
Therefore,
The series always absolutely for all real x
Since,
Therefore,
The series always converges for interval
Conclusion:
The series always converges for interval
(c)
The series
(c)
Answer to Problem 8RE
The series always converges absolutely for interval
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
Since,
Therefore,
The series always absolutely for all real x
Since,
Therefore,
The series always converges absolutely for interval
Conclusion:
The series always converges absolutely for interval
(d)
The series
(d)
Answer to Problem 8RE
The series always converges absolutely for all real x , there is no points of conditional convergence.
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
Since, the series always converges absolutely for all real x , there is no points of conditional convergence.
Conclusion:
The series always converges absolutely for all real x , there is no points of conditional convergence.
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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