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a.
To find: what can be said about the convergence or divergence of the following series.
a.
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Answer to Problem 26E
Converges.
Explanation of Solution
Given information: Suppose that
Calculation:
The Centre of convergence of the series
The Interval of convergence is of the form (- k, k )
One or both the end points may be included in the interval of convergence,
Since it is given that the series converges when x =-4, this implies that the series converges for all x which lie in the interval (-4, 4).
The series
b.
To find: what can be said about the convergence or divergence of the following series.
b.
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Answer to Problem 26E
Diverges.
Explanation of Solution
Given information: Suppose that
Calculation:
The Centre of convergence of the series
The Interval of convergence is of the form (- k, k )
One or both the end points may be included in the interval of convergence,
Since it is given that the series diverges when x =6, this implies that the series convergence is smaller than or equal to (-6, 6).
The series
c.
To find: what can be said about the convergence or divergence of the following series.
c.
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Answer to Problem 26E
Converges.
Explanation of Solution
Given information: Suppose that
Calculation:
The Centre of convergence of the series
The Interval of convergence is of the form (- k, k )
One or both the end points may be included in the interval of convergence,
Since it is given that the series converges when x =-4, this implies that the series converges for all x which lie in the interval (-4, 4).
The series
d.
To find: what can be said about the convergence or divergence of the following series.
d.
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Answer to Problem 26E
Diverges.
Explanation of Solution
Given information: Suppose that
Calculation:
The Centre of convergence of the series
The Interval of convergence is of the form (- k, k )
One or both the end points may be included in the interval of convergence,
Since it is given that the series diverges when x =6, this implies that the series convergence is smaller than or equal to (-6, 6).
The series
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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