Suppose that ak > 0 and that ak1/k as k . Prove that k=1 akxk

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Suppose that ak > 0 and that ak1/k → as k → ∞. Prove that ∑∞k=1 akxk converges absolutely for all |x| < 1/a if a ≠ 0 and for all x ∈ R if a = 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 04:07 AM

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Suppose that ak > 0 and that ak1/k as k . Prove that k=1 akxk

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Notice that k a k x k ka k x a x as k Hence if a 0 ...View the full answer

An Introduction to Analysis

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