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Easy Series Convergence LIFESAVER

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Scholar
Karma Points: 262
(University of Texas at Tyler)
Respect (99%):
Date Posted: 7/2/2008 9:44:37 PM  Status: Closed
Easy Series Convergence LIFESAVER
Course Textbook Chapter Problem
Calculus Calculus With Analytic Geometry (8th) by Edwards, Larson, Hostetler 9.2 36E
Question Details:
 
Use partial fractions,

 
               
 
and
∴ the series converges to 3


Last line: What convergence formula is he using? Or what is he plugging in to get 3?
Bonus Point Alert! Earn +4 additional karma points for helping this annual member.
 
Jordan Rey

Answers:

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Oracle
Karma Points: 33,668
(ANDHRA UNIVERSITY COLLEGE OF ENGINEERING)
Date Posted: 7/2/2008 9:58:45 PM  Status: Live
Asker's Rating: Lifesaver   
Response:
Question: 
=============================================================
∴ the series converges to 3
Last line: What convergence formula is he using? Or what is he plugging in to get 3?
===============================================================
THERE IS NO FORMULA USED.
FIRST THE INFINITE SUM WAS CONVERTED TO THE LIMIT OF A FUNCTION.
THE LIMIT IS TO BE EVALUATED NOW.
OBVIOUSLY 3 REMAINS AS 3 AS N TENDS TO INFINITY

HENCE THE SUM = 3-0=0
===============================================================



Use partial fractions,

 
               
 
and
∴ the series converges to 3
Jordan Rey's Comment:
Awesome. Thank you for your explanation


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Oracle
Karma Points: 16,173
Date Posted: 7/2/2008 10:01:54 PM  Status: Live
Asker's Rating: Helpful   
Response:
 
in the second term, we have do the following:
 
=
 
so

Don't forget give me good rating  to show your respect for my time to help you!



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