(a) Use differentiation to find a power series representation for 1 f(x) (6 + x)2 f(x) n = 0 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for 1 f(x) : (6 + x)3 %D f(x) n = 0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for x2 f(x) (6 + x)³ Σ ) 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
Section10.2: Arithmetic Sequences
Problem 67E
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(a) Use differentiation to find a power series representation for
1
f(x)
(6 + x)2
f(x)
n = 0
What is the radius of convergence, R?
R =
(b) Use part (a) to find a power series for
1
f(x) :
(6 + x)3
%D
f(x)
n = 0
What is the radius of convergence, R?
R =
(c) Use part (b) to find a power series for
x2
f(x)
(6 + x)³
Σ
)
f(x) = )
n = 2
What is the radius of convergence, R?
R =
Transcribed Image Text:(a) Use differentiation to find a power series representation for 1 f(x) (6 + x)2 f(x) n = 0 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for 1 f(x) : (6 + x)3 %D f(x) n = 0 What is the radius of convergence, R? R = (c) Use part (b) to find a power series for x2 f(x) (6 + x)³ Σ ) f(x) = ) n = 2 What is the radius of convergence, R? R =
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