Let (an) be a decreasing sequence of real numbers converging to 0 and suppose that an diverges.

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Let (an) be a decreasing sequence of real numbers converging to 0 and suppose that ∑an diverges. Construct a divergent series ∑bn with bn > 0 such that lim(bn/an)= 0; hence ∑bn diverges less rapidly than ∑an. [Let bn := an/√An where An is the nth partial sum of ∑an.]
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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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