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Old 10-30-2014, 06:27 PM   #6
seamonkey
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Default Re: The Positive Thread

Quote:
Originally Posted by Megadog View Post
It comes from the same math that makes 1 - 1 + 1 - 1 + 1 - 1 + ... = 1/2.

You then do 1 - 2 + 3 - 4 + 5 - 6 + ... = 2 * (1 - 1 + 1 - 1 + 1 - 1 + ...) = 1/4.

and then you have 1 + 2 + 3 + 4 + 5 + 6 + ... - 1 - 2 + 3 - 4 + 5 - 6 + ... = 4 + 8 + 12 + 16 + ... = 4*(1 + 2 + 3 + 4 + 5 + 6 + ...) => -1/4 = 3*(1 + 2 + 3 + 4 + 5 + 6 + ...) => 1 + 2 + 3 + 4 + 5 + 6 + ... = -1/12.

That's the best I can do in explaining it. This was taken from the numberphile video on the subject, which I can post because youtube.
Except that numberphile screwed it up. Adding and multiplying infinite series that diverge isn't something that is allowed.
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