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8. 2 (- 1)" x2" n=0

8. 2 (- 1)" x2" n=0

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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Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x.

8. 2 (- 1)" x2" n=0
Transcribed Image Text:8. 2 (- 1)" x2" n=0
Expert Solution
Step 1

Given: ∑n=0∞-1nx2n

for finding given summation, first we expand it by putting value of n=0,1,2,3,.........

so,

∑n=0∞-1nx2n=1-x2+x4-x6+x8+.....................            ..1

now, equation1 is infinite geometric progression whose first term is 1 and common ratio is -x2

we know that for infinite geometric progression to converge -x2<1⇒x2<1 

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