(a) Find a power series representation for f(x) = In(1 + x). f(x) = = - 80 ( − 1 ) n − 1 x n n = 1 n What is the radius of convergence, R? R = 1 (b) Use part (a) to find a power series for f(x) = x In(1 + x). f(x) = Σ n = 2 What is the radius of convergence, R? R = 1 (c) Use part (a) to find a power series for f(x) = In(x² + 1). f(x) = 8 n = 1 What is the radius of convergence, R? R = 1
(a) Find a power series representation for f(x) = In(1 + x). f(x) = = - 80 ( − 1 ) n − 1 x n n = 1 n What is the radius of convergence, R? R = 1 (b) Use part (a) to find a power series for f(x) = x In(1 + x). f(x) = Σ n = 2 What is the radius of convergence, R? R = 1 (c) Use part (a) to find a power series for f(x) = In(x² + 1). f(x) = 8 n = 1 What is the radius of convergence, R? R = 1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
Question
Transcribed Image Text:(a) Find a power series representation for f(x) = In(1 + x).
f(x) =
=
-
80
( − 1 ) n − 1 x n
n = 1
n
What is the radius of convergence, R?
R = 1
(b) Use part (a) to find a power series for f(x) = x In(1 + x).
f(x)
=
Σ
n = 2
What is the radius of convergence, R?
R = 1
(c) Use part (a) to find a power series for f(x) = In(x² + 1).
f(x) =
8
n = 1
What is the radius of convergence, R?
R = 1
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