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July 11th, 2012, 11:29 AM  #1 
Newbie Joined: Jun 2012 Posts: 26 Thanks: 0  Infinite Series
If you have an infinite series, does it matter in what order you add the terms?

July 11th, 2012, 11:32 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Infinite Series
No, the commutative property of addition allows the addends to be arranged in any possible order.

July 11th, 2012, 12:27 PM  #3  
Global Moderator Joined: May 2007 Posts: 6,821 Thanks: 723  Re: Infinite Series Quote:
An example (conditionally convergent) 1  1/2 + 1/3  1/4 + 1/5  1/6 + ..... Rearranging terms can produce any answer.  
July 11th, 2012, 04:54 PM  #4  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Infinite Series Hello, Mathforum1000! Quote:
If the terms are all positive, the answer is Yes. If it is an alternating series, the answer is Maybe. There is a classic fallcy that depends on overlooking this fact. I believe this is what mathman referred to. [color=beige]. . . . . . . . . . . . . .[/color] [color=beige]. . . . [/color] [color=beige]. . . . [/color] [color=beige]. . . . [/color]  
July 12th, 2012, 04:25 AM  #5  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Infinite Series Quote:
 

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