Concept explainers
(a)
The interval of convergence for the series is
(a)
Answer to Problem 4QQ
The interval of convergence is - 5 < x < 1
Explanation of Solution
Given information:
The given series is
Formula used:
The geometric series with common ratio
Calculation:
If the sequence of partial sum has a limit as
The given is a geometric series with common ratio
Therefore,
That gives
Therefore,
The interval of convergence is - 5 < x < 1
Conclusion:
The interval of convergence is - 5 < x < 1
(b)
The series that the function f represents.
(b)
Answer to Problem 4QQ
The function represented by the series is,
Explanation of Solution
Given information:
The given series is
Formula used:
Calculation:
The sum of the infinite geometric series whose ratio is <1.
Therefore, sum of the series is
And the function represented by the series is,
Where,
Conclusion:
The function represented by the series is,
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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