a.
To find:The interval of convergence of given series.
a.
Answer to Problem 41E
The series
Explanation of Solution
Given:
The given series is
Formula/ concept used:
Ratio Test: Suppose
Calculations:
The given series is
Now,
The series (1) is convergent if
Now, for
Hence, the series
Conclusion:
The series
b.
To find:The values of x for which the series
b.
Answer to Problem 41E
The series
Explanation of Solution
Given:
Theseries
Concept used:
Suppose
Calculations:
The given series is
As shown in part (a)
Therefore, the series
Conclusion:
The series
c.
To find: The value of x for which the series
c.
Answer to Problem 41E
There is no interval in which the series converge conditionally.
Explanation of Solution
Given:
The series
Concept used:
The series
If the original series
If a series is alternating and not absolutely convergent, we check for conditional convergence using the alternating series test.
Calculations:
As shown in part (a) and (b) the series
Since, the series
Conclusion:
There is no interval in which the series converge conditionally.
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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