(a)
the radius of the convergence is
(a)
Answer to Problem 5RE
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 5RE
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 5RE
The series always converges absolutely 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 absolutely for interval
Conclusion:
The series always converges absolutely for interval
(d)
The series
(d)
Answer to Problem 5RE
There is no point of conditional convergence.
Explanation of Solution
Given information:
The given series is,
Formula used:
Ratio test is used.
Calculation:
There is no point of conditional convergence.
Conclusion:
There is no point of conditional convergence.
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
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Calculus: Early Transcendentals (3rd Edition)
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