The preceding exercise may fail if the terms are not positive. For example, let aij := +1

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The preceding exercise may fail if the terms are not positive. For example, let aij := +1 if i - j = 1, aij := -1 if i - j = -1, and aij := 0 elsewhere. Show that the iterated sums
α j=1 =1 and aυ =i j=1 ΣΣ ΣΣ

Both exist but are not equal.

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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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