4. Let En an be an absolutely convergent series. Prove that if p > 1 then the series En a converge absolutely. Give an example in which if 0 < p<1, then En a can either converge or diverge. Be sure to justify.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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4. Let En an be an absolutely convergent series. Prove that if p > 1 then the series na
converge absolutely. Give an example in which if 0 < p< 1, then Σ a can either converge
or diverge. Be sure to justify.
Transcribed Image Text:4. Let En an be an absolutely convergent series. Prove that if p > 1 then the series na converge absolutely. Give an example in which if 0 < p< 1, then Σ a can either converge or diverge. Be sure to justify.
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