Question
Asked Nov 22, 2019
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Find the power series representation for g(x) centered at 0 by differentiating or integrating the power series for f(x). Give the interval of convergence for the resulting series.

f(x) = [1/(1-x)]   ;   g(x) = [1/(1-x)3]

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Expert Answer

Step 1
1
The given functions are f(x
1
and g(x)
1-x
(1-х)
The power series representation for the function f (x) =x" and the radius
of convergence is x|<1.
d
1
and use the fact
1
1
Consider f(x)=-
d1-x
1-x
d
1
1
d1-x
d
1
1
d1-x
-
1
Σ"
(1-x)
dx
1
-nx'
=
(1-x)*
1=1
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Image Transcriptionclose

1 The given functions are f(x 1 and g(x) 1-x (1-х) The power series representation for the function f (x) =x" and the radius of convergence is x|<1. d 1 and use the fact 1 1 Consider f(x)=- d1-x 1-x d 1 1 d1-x d 1 1 d1-x - 1 Σ" (1-x) dx 1 -nx' = (1-x)* 1=1

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