(a) Use differentiation to find a power series representation for f(x): = f(x): 8 = Σ(1 n = 0 f(x) What is the radius of convergence, R? R = 4 (b) Use part (a) to find a power series for 1 (4 + x)3* 1 (4 + x)² = 8 f(x) = Σ( n = 0 8 f(x) = = X 4 What is the radius of convergence, R? R = 4 (c) Use part (b) to find a power series for x² (4 + x)³ X f(x) = ((-1)" Σ n = 2 n(n-1) 2.4"+1 -xn What is the radius of convergence, R? R = 4
(a) Use differentiation to find a power series representation for f(x): = f(x): 8 = Σ(1 n = 0 f(x) What is the radius of convergence, R? R = 4 (b) Use part (a) to find a power series for 1 (4 + x)3* 1 (4 + x)² = 8 f(x) = Σ( n = 0 8 f(x) = = X 4 What is the radius of convergence, R? R = 4 (c) Use part (b) to find a power series for x² (4 + x)³ X f(x) = ((-1)" Σ n = 2 n(n-1) 2.4"+1 -xn What is the radius of convergence, R? R = 4
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
Related questions
Question
![(a) Use differentiation to find a power series representation for
f(x)
=
f(x):
8
Σ(
n = 0
f(x) =
What is the radius of convergence, R?
R = 4
8
f(x) = Σ (
n = 0
(b) Use part (a) to find a power series for
1
(4 + x)3*
1
(4 + x)²
1/14
f(x)
8
X
=
4
What is the radius of convergence, R?
R =
4
(c) Use part (b) to find a power series for
x²
(4 + x)³*
X
f(x) = Σ( (-1)n n(n − 1)
2.4"+1
n = 2
-x"
What is the radius of convergence, R?
R = 4
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0f3a834-d342-4869-9dbf-9d566abb1119%2F3bde3653-2410-4fc8-979a-14684875a85f%2F676r6zo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Use differentiation to find a power series representation for
f(x)
=
f(x):
8
Σ(
n = 0
f(x) =
What is the radius of convergence, R?
R = 4
8
f(x) = Σ (
n = 0
(b) Use part (a) to find a power series for
1
(4 + x)3*
1
(4 + x)²
1/14
f(x)
8
X
=
4
What is the radius of convergence, R?
R =
4
(c) Use part (b) to find a power series for
x²
(4 + x)³*
X
f(x) = Σ( (-1)n n(n − 1)
2.4"+1
n = 2
-x"
What is the radius of convergence, R?
R = 4
X
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