a) Suppose that k=1 ak converges absolutely. Prove that k=1 |ak|p converges for all p > 1.

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a) Suppose that ∑∞k=1 ak converges absolutely. Prove that ∑∞k=1 |ak|p converges for all p > 1. b) Suppose that ∑∞k=1 ak converges conditionally. Prove that ∑∞k=1 kpak diverges for all p > 1.

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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 04:07 AM

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a) Suppose that k=1 ak converges absolutely. Prove that k=1 |ak|p converges for all p > 1.

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a Since ak 0 as k ak 1 for k large Hence ak p a k for k large and it f...View the full answer

An Introduction to Analysis

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