(a) Find a power series representation for f(x) = In(1 + x). 1e) Σ( n = 1 f(x) : What is the radius of convergence, R? 2 %D (b) Use part (a) to find a power series for f(x) = x In(1 + x). Σ f(x) = n = 2 What is the radius of convergence, R? R = 4 (c) Use part (a) to find a power series for f(x) = In(x2 + 1). Σ f(x) = n = 1 What is the radius of convergence, R?
(a) Find a power series representation for f(x) = In(1 + x). 1e) Σ( n = 1 f(x) : What is the radius of convergence, R? 2 %D (b) Use part (a) to find a power series for f(x) = x In(1 + x). Σ f(x) = n = 2 What is the radius of convergence, R? R = 4 (c) Use part (a) to find a power series for f(x) = In(x2 + 1). Σ f(x) = n = 1 What is the radius of convergence, 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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Transcribed Image Text:(a) Find a power series representation for f(x) = In(1 + x).
1e) Σ(
n = 1
f(x) :
What is the radius of convergence, R?
2
%D
(b) Use part (a) to find a power series for f(x) = x In(1 + x).
Σ
f(x) =
n = 2
What is the radius of convergence, R?
R = 4
(c) Use part (a) to find a power series for f(x) = In(x2 + 1).
Σ
f(x) =
n = 1
What is the radius of convergence, R?
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