a.
To find: the interval of convergence of the series.
a.
Answer to Problem 47E
Interval of convergence is
Explanation of Solution
Given:
Formula used:
Power series about
If
For convergent series the limit will result in
Calculation:
Applying limit we get,
As
The radius of convergence is
Interval of convergence will be:
The interval of convergence is
b.
To find: Values of x for which the series converges absolutely.
b.
Answer to Problem 47E
The series converges absolutely for interval
Explanation of Solution
Given:
Formula used:
Power series about
For convergent series the limit will result in
The series converges absolutely for the values of x in the interval of convergence.
Calculation:
From part a, the interval of convergence is
Thus the series converges absolutely for values of x belonging in the interval
c.
To find: Values of x for which the series converges conditionally.
c.
Answer to Problem 47E
The series does not converge conditionally at any point.
Explanation of Solution
Given:
Formula used:
Power series about
For convergent series the limit will result in
The series converges at end points then the series converges conditionally at that points.
Calculation:
Test the end points of the interval of convergence,
At
The series diverges.
At
The series diverges.
Therefore, the series does not converge conditionally anywhere.
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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