(a) Prove that if )ak converges absolutely and (bk) is a subsequence of (ak) then > bk alsok=1k=1converges absolutely.(b) Show by example that (a) does not hold if we only require that > ak converge conditionally.k=1

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Answered: (a) Prove that if > ak converges…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 72E

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(a) Prove that if > ak converges absolutely and (bk) is a subsequence of (ar) then ) bk also k=1 k=1 converges absolutely. (b) Show by example that (a) does not hold if we only require that >ak converge conditionally. k=1