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(a) Find a power series representation for f(x) = In(1+x). 00 f(x) = Σ( n = 1 What is the radius of convergence, R? R= (b) Use part (a) to find a power series for f(x) = x ln(1 + x). 00 f(x) = Σ( n=2 What is the radius of convergence, R? R = (c) Use part (a) to find a power series for f(x) = In(x² + 1). f(x) = Σ ( n=1 What is the radius of convergence, R? R =

(a) Find a power series representation for f(x) = In(1+x). 00 f(x) = Σ( n = 1 What is the radius of convergence, R? R= (b) Use part (a) to find a power series for f(x) = x ln(1 + x). 00 f(x) = Σ( n=2 What is the radius of convergence, R? R = (c) Use part (a) to find a power series for f(x) = In(x² + 1). f(x) = Σ ( n=1 What is the radius of convergence, R? R =

Algebra & Trigonometry with Analytic Geometry
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) Find a power series representation for f(x) = In(1 + x). 00 f(x) = n = 1 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for f(x) = x ln(1 + x). 00 F(x) = Σ( n = 2 What is the radius of convergence, R? R = (c) Use part (a) to find a power series for f(x) = In(x² + 1). 00 f(x) = Σ( n = 1 What is the radius of convergence, R? R =
Transcribed Image Text:(a) Find a power series representation for f(x) = In(1 + x). 00 f(x) = n = 1 What is the radius of convergence, R? R = (b) Use part (a) to find a power series for f(x) = x ln(1 + x). 00 F(x) = Σ( n = 2 What is the radius of convergence, R? R = (c) Use part (a) to find a power series for f(x) = In(x² + 1). 00 f(x) = Σ( n = 1 What is the radius of convergence, R? R =
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