   Chapter 9.9, Problem 40E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Using a Power Series In Exercises 37-40, use the power series 1 1 − x = ∑ n = 0 ∞ x n ,         | x |   < 1 to find a power aeries for the function, centered at 0, and determine the interval of convergence. f ( x ) = x ( 1 + x ) ( 1 − x ) 2

To determine

To calculate: The power series of f(x)=x(1+x)(1x)2 centered at 0 and determine the interval of convergence.

Explanation

Given:

The function is f(x)=x(1+x)(1x)2

Formula used:

Power series is:11x=n=0xn,|x|<1, 1(1x)2=n=0(n+1).xn, 1(1x)2=n=0nxn

Calculation:

Since,

11x=n=0xn,|x|<1

So,

x(1+x)(1x)2=x+x2(1x)2=x(

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