3. Show that the power series (a)-(c) have the same radius of convergence. Then show that (a) diverges at both endpoints, (b) converges at one endpoint but diverges at the other, and (c) converges at both endpoints. x" п3 x" (c) n23n (a) x" (b) n=1 n=1 n=1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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3. Show that the power series (a)-(c) have the same radius of convergence. Then show that (a) diverges at
both endpoints, (b) converges at one endpoint but diverges at the other, and (c) converges at both endpoints.
x"
п3
x"
(c)
n23n
(a)
x"
(b)
n=1
n=1
n=1
Transcribed Image Text:3. Show that the power series (a)-(c) have the same radius of convergence. Then show that (a) diverges at both endpoints, (b) converges at one endpoint but diverges at the other, and (c) converges at both endpoints. x" п3 x" (c) n23n (a) x" (b) n=1 n=1 n=1
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