If k=1 akxk has radius of convergence R and ak 0 for large prove that lim inf|-|

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If ˆ‘ˆžk=1 akxk has radius of convergence R and ak ‰ 0 for large prove that

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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 04:10 AM

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Suppose that k=0 akxk has radius of convergence R (0, ). a) Find the radius of convergence of k=0 akx2k. b) Find the radius of convergence of k=0 a2kxk .
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If k=1 akxk has radius of convergence R and ak 0 for large prove that lim inf|-|

Question:

lim inf|-| < R < lim sup |--.

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Suppose lim sup a k a k 1 R By Exercise 258 lim inf a k1 a k 1r for some r R He...View the full answer

An Introduction to Analysis

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