(a) Use differentiation to find a power series representation for 1 f(x) (8 x)2 + co f(x) n0 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for 1 f(x) (8 x)3 00 f)-Σ( = n 0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for x2 (8 x)3 f(x) co re)-Σ( n2 What is the radius of convergence, R? R =

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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(a) Use differentiation to find a power series representation for
1
f(x)
(8 x)2
+
co
f(x)
n0
What is the radius of convergence, R?
R =
(b) Use part (a) to find a power series for
1
f(x)
(8 x)3
00
f)-Σ(
=
n 0
What is the radius of convergence, R?
R =
(c) Use part (b) to find a power series for
x2
(8 x)3
f(x)
co
re)-Σ(
n2
What is the radius of convergence, R?
R =
Transcribed Image Text:(a) Use differentiation to find a power series representation for 1 f(x) (8 x)2 + co f(x) n0 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for 1 f(x) (8 x)3 00 f)-Σ( = n 0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for x2 (8 x)3 f(x) co re)-Σ( n2 What is the radius of convergence, R? R =
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