To calculate: The radius of convergence of the power series.
Answer to Problem 34E
The radius of convergence of the power series is
Explanation of Solution
Given information:
The radius of convergence of the series
Concept Used:
Ratio Test:
(i) If
(and therefore convergent)
(ii) If
(iii) If
Calculation:
The series given is
Then apply ratio test to this
The series is conversent if the value of
Therefore
So, the radius of convergence
Then
For the series
Put the value in this equation
Then,
The series is conversent if the value of
Therefore,
So, the radius of convergence of the power series is
Conclusion:
The radius of convergence of the power series is
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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