(a)
the radius of the convergence
(a)
Answer to Problem 4RE
The radius of convergence for is
Explanation of Solution
Given information:
The given function is,
Formula 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 radius of the convergence
(b)
Answer to Problem 4RE
The series always converges for interval
Explanation of Solution
Given information:
The given function 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 4RE
The series is always converges absolutely for interval
Explanation of Solution
Given information:
The given function is,
Formula used:
Ratio test is used.
Calculation:
Since,
Therefore the series always converges absolutely for all real x
Since,
Therefore, the series is always converges absolutely for interval
Conclusion:
The series is always converges absolutely for interval
(d)
the series
(d)
Answer to Problem 4RE
There is no point of conditional convergence.
Explanation of Solution
Given information:
The given function is,
Formula used:
Ratio test is used.
Calculation:
Since, the series always converges absolutely for all real x, 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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