My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 17th, 2011, 05:51 PM   #1
Senior Member
 
Joined: Sep 2011
From: New York, NY

Posts: 333
Thanks: 0

Series Divergence Theorem

I have a question about the divergence theorem that has confused me for some time.

The divergence theorem says



This seems to be contradicted in the example for a telescoping series below. Here they say that goes to 1, and the series sum is one.

aaron-math is offline  
 
December 17th, 2011, 05:55 PM   #2
Senior Member
 
Joined: Oct 2011
From: Belgium

Posts: 522
Thanks: 0

Re: Series Divergence Theorem



I don't see the contradiction.
wnvl is offline  
December 17th, 2011, 05:59 PM   #3
Senior Member
 
Joined: Sep 2011
From: New York, NY

Posts: 333
Thanks: 0

Re: Series Divergence Theorem

here

aaron-math is offline  
December 17th, 2011, 06:02 PM   #4
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 520

Math Focus: Calculus/ODEs
Re: Series Divergence Theorem

But and as wnvl pointed out, .

However, and so .

You are confusing with .
MarkFL is offline  
December 17th, 2011, 06:15 PM   #5
Senior Member
 
Joined: Sep 2011
From: New York, NY

Posts: 333
Thanks: 0

Re: Series Divergence Theorem

ok, I think I see now.

is the sequence of terms. The Nth them must be zero otherwise you will never stop adding to the series, and it will have to diverge.

is the partial sum of the first n-terms.

It is confusing because all we are doing is putting in a another form and saying now it's now zero it's one.
aaron-math is offline  
December 17th, 2011, 06:27 PM   #6
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 520

Math Focus: Calculus/ODEs
Re: Series Divergence Theorem

Yes:



So, by the theorem cited above, we know the infinite series is divergent if . This does not mean necessarily however, that the infinite series converges if .

Once we've established it diverges then we are done, but if the test for divergence fails, then we must prove whether it converges or not through the various tests for convergence.
MarkFL is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
divergence, series, theorem



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Question in Stokes and Divergence theorem. alan0354 Applied Math 0 August 10th, 2013 09:14 AM
series divergence walter r Real Analysis 4 May 4th, 2013 07:34 PM
Divergence of a series patient0 Real Analysis 5 December 11th, 2010 06:17 AM
Convergence/Divergence of an Infinite Series everettjsj2 Calculus 3 February 28th, 2010 04:36 PM
Series divergence HammerTime Real Analysis 1 November 20th, 2008 04:18 AM





Copyright © 2019 My Math Forum. All rights reserved.