To calculate: The radius of the convergence of the series.
Answer to Problem 27E
The radius of the convergence of the series is
Explanation of Solution
Given information:
Concept Used:
Ratio Test:
(i) If
(and therefore convergent)
(ii) If
(iii) If
Calculation:
The series is
Then,
By use of ratio test
The series converges if the result of the ratio test is
So,
The radius of convergence is the half the width of the interval.
Conclusion:
The radius of the convergence of the series is
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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