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#1 2011-06-18 03:28:34

anonimnystefy
Real Member

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Grandi's series (1-1+1-1...)

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 (2011-06-18 03:28:48)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#2 2011-06-18 14:25:36

soroban
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Re: Grandi's series (1-1+1-1...)








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#3 2011-07-10 14:58:30

MathPro101
Member

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Re: Grandi's series (1-1+1-1...)

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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