(a) Use differentiation to find a power series representation for f(x) = f(x) = n = 0 What is the radius of convergence, R? R = f(x) = (b) Use part (a) to find a power series for 1 (6 + x)³ f(x) = 1 (6 + x)2 Σ n=0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for x² (6 + x)³ f(x) = f(x) = n = 2 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
Section10.3: Geometric Sequences
Problem 50E
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(a) Use differentiation to find a power series representation for
f(x) =
f(x)
3-
=
00
Σ
n = 0
What is the radius of convergence, R?
R =
f(x) =
(b) Use part (a) to find a power series for
1
(6 + x)
f(x) =
00
f(x) = Σ
n = 0
1
(6 + x)2 °
What is the radius of convergence, R?
R =
(c) Use part (b) to find a power series for
x2
(6 + x)3.
f(x)
Σ(
η = 2
What is the radius of convergence, R?
R =
Transcribed Image Text:(a) Use differentiation to find a power series representation for f(x) = f(x) 3- = 00 Σ n = 0 What is the radius of convergence, R? R = f(x) = (b) Use part (a) to find a power series for 1 (6 + x) f(x) = 00 f(x) = Σ n = 0 1 (6 + x)2 ° What is the radius of convergence, R? R = (c) Use part (b) to find a power series for x2 (6 + x)3. f(x) Σ( η = 2 What is the radius of convergence, R? R =
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