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July 11th, 2012, 11:29 AM   #1
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Infinite Series

If you have an infinite series, does it matter in what order you add the terms?
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July 11th, 2012, 11:32 AM   #2
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Re: Infinite Series

No, the commutative property of addition allows the addends to be arranged in any possible order.
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July 11th, 2012, 12:27 PM   #3
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Re: Infinite Series

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Originally Posted by Mathforum1000
If you have an infinite series, does it matter in what order you add the terms?
It might. If the series is absolutely convergent, then it does not matter. If it is conditionally convergent it will.

An example (conditionally convergent) 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ..... Rearranging terms can produce any answer.
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July 11th, 2012, 04:54 PM   #4
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Re: Infinite Series

Hello, Mathforum1000!

Quote:
If you have an infinite series, does it matter in what order you add the terms?

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.






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July 12th, 2012, 04:25 AM   #5
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Re: Infinite Series

Quote:
If you have an infinite series, does it matter in what order you add the terms?






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