a) Prove that k=1 sin(x/k2) converges uniformly on any bounded interval in R. b) Prove that k=0e-kx

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a) Prove that ∑∞k=1 sin(x/k2) converges uniformly on any bounded interval in R.
b) Prove that ∑∞k=0e-kx converges uniformly on any closed subinterval of (0, ∞).

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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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a) Prove that k=1 sin(x/k2) converges uniformly on any bounded interval in R. b) Prove that k=0e-kx

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a Since sinxk 2 xk 2 maxa bk 2 for any x a b this series co...View the full answer

An Introduction to Analysis

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