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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

Grandi's series is the infinite sum: 1-1+1-1...

What's interesting about it is that it cna have several 'values':

1. We can group the terms like this:

(1-1)+(1-1)...=0+0+0+0+0+...=0

2. We can group the terms this way:

1+(-1+1)+(-1+1)...=1+0+0+...=1

3. The final way that I know of is to have s be equal to the sum:

s=1-1+1-1...

s=1+(-1+1-1...)

s=1-(1-1+1-1...)

s=1-s

2s=1

s=1/2

which is quite an unusual answer.

http://en.wikipedia.org/wiki/Grandi's_series

*Last edited by anonimnystefy (2011-06-17 05:28:48)*

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**soroban****Member**- Registered: 2007-03-09
- Posts: 452

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**MathPro101****Member**- Registered: 2011-06-08
- Posts: 18

Question: When I explained Grandi's series to a friend, they stated that addition is commutative, which is true. They wanted to know why the commutative property is allowed to be violated for this series. I suggested that it has to do with the fact that it is a series, and not just any normal addition. Could anyone help me explain why we don't break any laws? Thank you.

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