(a)
The values of x by which the series converges absolutely.
(a)
Answer to Problem 4QQ
The series converges absolutely on (-2, -1)
Explanation of Solution
Given information:
The given function is,
Formula used:
Ratio test is used
Calculation:
Check for absolute convergence using ratio test.
Hence,
Therefore,
That gives
Therefore, series converges absolutely on (-2, -1)
Conclusion:
The series converges absolutely on (-2, -1)
(b)
The values of x by which the series converges conditionally.
(b)
Answer to Problem 4QQ
There are no values of x for which the series converges conditionally.
Explanation of Solution
Given information:
The given function is,
Formula used:
Ratio test is used.
Calculation:
Checking convergence at end points
At
Therefore nth term test fails. Therefore series diverges at x = -2
At
Therefore,
nthterm test fails. Therefore series diverges at x=2
Since, the series converges absolutely on (-2,-1) and diverges at both the end points. There are no values of x for which the series converges conditionally.
Conclusion:
The series converges absolutely on (-2,-1) and diverges at both the end points. There are no values of x for which the series converges conditionally.
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus and Its Applications (11th Edition)
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