x2 f(x)= What is the power series representation of the function f(x) and the range of convergence of this series? (3-х) (a) E n.x n.xn+2 3n+2 - 3 n.x n+1 -1

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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x2
f(x) =-
(3-х
What is the power series representation of the function f(x)
and the range of convergence of this series?
n.x"
(a) E
3n
-3<x <3
n.x"
n+2
(b) E
3n+2
- 3<x <3
n=1
n=1
(c) E
3n+2
n.xn+2
n+1
n.x
-1<x <1
(d) E
3n+1
-3 <x <3
n=1
n=1
n+1
n.x
Σ
3n+1
(e)
-1<x <1
n=1
Transcribed Image Text:x2 f(x) =- (3-х What is the power series representation of the function f(x) and the range of convergence of this series? n.x" (a) E 3n -3<x <3 n.x" n+2 (b) E 3n+2 - 3<x <3 n=1 n=1 (c) E 3n+2 n.xn+2 n+1 n.x -1<x <1 (d) E 3n+1 -3 <x <3 n=1 n=1 n+1 n.x Σ 3n+1 (e) -1<x <1 n=1
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