The interval of convergence of the series
Answer to Problem 45E
The interval of convergence and series converges absolutely on
Explanation of Solution
Given information:
The given series is
Formula used:
The ratio test is used.
Calculation:
The series of absolute values is
The ratio Test let
Then, the series converges if L < I, the series diverges if L >1 and the test is inconclusive if L=1
Using the ratio test, we check for absolute convergence as follows,
The series converges absolutely for
And diverges for
And when |x | = 3, the series diverges by the nth-term test
(a) Interval of convergence:
(b) Series converges absolutely on
(c) None
Conclusion:
The interval of convergence and series converges absolutely on
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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