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1 Find a power series representation of a (1– x)2 * | +00 1 %3D 2 3 + 22 ' 23 b Find the sum of the series > - n=1 2n II

1 Find a power series representation of a (1– x)2 * | +00 1 %3D 2 3 + 22 ' 23 b Find the sum of the series > - n=1 2n II

Calculus: Early Transcendentals
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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Why was x = 1/2 plugge din the equations?

1 Find a power series representation of a (1— х)2 +oo n 1 3 Find the sum of the series > 2" 22 ' 23 n=1 Solution. By multiplying the identity obtained in (a) by x, we obtain +oo E nx", for all x€ (-1,1). (1– x)² n=1 By plugging-in x= € (-1,1), we get %3D +oo n 1/2 = 2. 2" (1 – 1/2)² | n=1
Transcribed Image Text:1 Find a power series representation of a (1— х)2 +oo n 1 3 Find the sum of the series > 2" 22 ' 23 n=1 Solution. By multiplying the identity obtained in (a) by x, we obtain +oo E nx", for all x€ (-1,1). (1– x)² n=1 By plugging-in x= € (-1,1), we get %3D +oo n 1/2 = 2. 2" (1 – 1/2)² | n=1
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