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Ratio Test

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Scholar
Karma Points: 200
Respect (98%):
Date Posted: 7/24/2008 11:07:22 PM  Status: Live
Ratio Test
Course Textbook Chapter Problem
N/A N/A N/A N/A
Question Details:
use ratio test to find radius of convergence and interval of convergence of the power series



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Oracle
Karma Points: 8,939
Date Posted: 7/24/2008 11:34:15 PM  Status: Live
Asker's Rating: Lifesaver   
Response:




Simplify:

Pull out |x|, since limit only applies to n:

The limit goes to 0 and since 0 is always less than 1 the convergence is for all real numbers.

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Sage
Karma Points: 5,455
(Melbourne University)
Date Posted: 7/24/2008 11:54:09 PM  Status: Live
Asker's Rating: Helpful   
Response:
 


.........................................>cancel the like terms
we are left with


The ratio must be smaller than zero for series to be convergent
....................................................>radius of convergence =1
and interval of convergence of the power series is R




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