(a)
The radius of convergence of the series
(a)
Answer to Problem 15RE
The radius or convergence for it is 0.
Explanation of Solution
Given information:
The given series is,
Formula used:
Calculation:
Check for absolute convergence using ratio test.
Therefore, the series is convergent only for x = 0. Therefore, the radius or convergence for it is 0.
Conclusion:
The radius or convergence for it is 0.
(b)
The interval of convergence of the series
(b)
Answer to Problem 15RE
The series is convergent only at
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
Since,
Only for x = 0, only for x = 0. Therefore, the series is convergent only at
Conclusion:
The series is convergent only at
(c)
The series
(c)
Answer to Problem 15RE
The series is absolutely convergent only at
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
Since,
Only for x = 0. Therefore, the series is absolutely convergent only at
Conclusion:
The series is absolutely convergent only at
(d)
The series
(d)
Answer to Problem 15RE
There is no point of conditional convergence.
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
Since, the series is convergent only at x = 0, there is no point of conditional convergence.
Conclusion:
There is no point of conditional convergence.
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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