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Give an example of a series centered at 3 that only converges at its center and justify your answer.

Give an example of a series centered at 3 that only converges at its center and justify your answer.

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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Power series! Please show all work and fully justify how you got the answer! I would greatly appreciate any help with this as I get confused!

Give an example of a series centered at 3 that only converges at its center and justify your answer.
Transcribed Image Text:Give an example of a series centered at 3 that only converges at its center and justify your answer.
Expert Solution
Step 1

A series of the form-

∑n=1∞cnxn=c0+c1x+c2x2+c3x3+⋯

is a power series centered at x=0.

A series of the form-

∑n=1∞cnx-an=c0+c1x-a+c2x-a2+c3x-a3+⋯

is a power series centered at x=a.

To make this definition precisely we stipulate that x0=1 and x-a0=1even when x=0 and x=a respectively.

 

 

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