Suppose that ak ≥ 0 and that ak^1/3→ a as k → ∞.Prove that sigma,k from 1 to ∞,akx^k converges absolutely for all |x| < 1/a if a ≠ 0 and for all x ∈ R if a = 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Suppose that ak ≥ 0 and that ak^1/3→ a as k → ∞.Prove that sigma,k from 1 to ∞,akx^k converges absolutely for all |x| < 1/a if a ≠ 0 and for all x ∈ R if a = 0

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