3. ( for ) Find the power series representation f(x) = Σen(x - a)" n=0 f(x) = = 1 about x=a=0. Also determine the Interval of Convergence of the series. Hint: You may use the result from Geometric Series: X X 1+x5 = Σx", |x| < 1 n=0

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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3. (
for
) Find the power series representation
∞
f(x) = Σen(x − a)"
- Σ₁xx
n=0
f(x)
1
X
=
about x=a=0.
Also determine the Interval of Convergence of the series.
Hint: You may use the result from Geometric Series:
=
8
1+x5
∞
Σx", |x| < 1
n=0
Transcribed Image Text:3. ( for ) Find the power series representation ∞ f(x) = Σen(x − a)" - Σ₁xx n=0 f(x) 1 X = about x=a=0. Also determine the Interval of Convergence of the series. Hint: You may use the result from Geometric Series: = 8 1+x5 ∞ Σx", |x| < 1 n=0
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