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39. (a) Show that Σeak converges for each α > 0. (b) Show that keak converges for each a > 0. k=0 (c) Show that, more generally, Σk"eak converges for each k=0 nonnegative integer n and each a > 0.

39. (a) Show that Σeak converges for each α > 0. (b) Show that keak converges for each a > 0. k=0 (c) Show that, more generally, Σk"eak converges for each k=0 nonnegative integer n and each a > 0.

Algebra & Trigonometry with Analytic Geometry
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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39. (a) Show that Σeak converges for each α > 0. (b) Show that keak converges for each a > 0. k=0 (c) Show that, more generally, Σk"eak converges for each k=0 nonnegative integer n and each a > 0.
Transcribed Image Text:39. (a) Show that Σeak converges for each α > 0. (b) Show that keak converges for each a > 0. k=0 (c) Show that, more generally, Σk"eak converges for each k=0 nonnegative integer n and each a > 0.
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