a.
To find: The interval of convergence of the series.
a.
Answer to Problem 47E
The interval of convergence of the series is
Explanation of Solution
Given information:
Calculation:
By applying the Ratio Test and looking at the interval's endpoints, one can determine the interval where the series will converge.
Taking the absolute value of the terms in the series and looking at the following limit, only using the Ratio Test for series with non-negative terms.
The series converges absolutely based on the previous step if
The left endpoint of the interval is given by,
Where,
This series diverges because its general term does not approach zero, hence the series does not converge at the left endpoint. However, because it has only positive terms, it is absolutely convergent if it converges and it never converges conditionally.
The right endpoint of the interval is given by,
Where,
The series does not absolutely converge at the right endpoint since the
From the above steps it is known that,
The interval of convergence of the series is,
Therefore, the interval of convergence of the series is
b.
To find: For what value of
b.
Answer to Problem 47E
The value of
Explanation of Solution
Given information:
Calculation:
From part (a) it is known that,
The interval on which the series converges absolutely is given by,
Using the Ratio test,
The series diverges if,
Then, the series converges absolutely on
Therefore, the value of
c.
To find: For what value of
c.
Answer to Problem 47E
The value of
Explanation of Solution
Given information:
Calculation:
As identified the interval on which the series converges and converges absolutely in parts (a) and (b).
It is concluded that there is no value of
Therefore, there does not exist a value of
Chapter 9 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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