Suppose that f = k=1 fk converges uniformly on a set E R. If g1 is

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Suppose that f = ∑∞k=1 fk converges uniformly on a set E ⊂ R. If g1 is bounded on E and gk(x) > gk+1(x) > 0 for all x ∈ E and k ∈ N, prove that ∑∞k=1 fkgk converges uniformly on E.

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 04:09 AM

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Suppose that f = k=1 fk converges uniformly on a set E R. If g1 is

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Let F nm n km f k Choose M 0 so large that g 1 x M for x E Since ...View the full answer

An Introduction to Analysis

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