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: Graphical, Numerical, Algebraic
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