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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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Is it possible for an alternating series to converge

Chapter 10, Problem 9E

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QUESTION:

Is it possible for an alternating series to converge absolutely, but not conditionally?

Questions & Answers

QUESTION:

Is it possible for an alternating series to converge absolutely, but not conditionally?

ANSWER:

SOLUTION

STEP 1

Is it possible for an alternating series to converge absolutely, but not conditionally?

STEP 2

DEFINITION:

Absolute convergence:

A series   converges absolutely if the series of the absolute values,  converges.

Conditional convergence:

A series is said to converge conditionally if exist and is a finite number but

Step 3

Let us take an example of an alternating series.

   this is an alternating series.

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