2. (a) Use differentiation to find a power series representation for 1 f(x) = 1+1)" (1+x)² What is the radius of convergence? (b) Use part (a) to find a power series for f(x) = (1+ x)³ (c) Use part (b) to find a power series for f(r) = (1 + 2)3

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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2. (a) Use differentiation to find a power series representation for
1
f(x) = 1+1)"
%3D
(1+x)²
What is the radius of convergence?
(b) Use part (a) to find a power series for
1
f(x) =
(1+ x)³
(c) Use part (b) to find a power series for
f(r) =
(1+ 2)3
Transcribed Image Text:2. (a) Use differentiation to find a power series representation for 1 f(x) = 1+1)" %3D (1+x)² What is the radius of convergence? (b) Use part (a) to find a power series for 1 f(x) = (1+ x)³ (c) Use part (b) to find a power series for f(r) = (1+ 2)3
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