TWCP OTD - 9th of March, 2017

[Kornfeld Eliyahu Peter]

TRUE MATH Try to prove it... 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 ... (and goes for the infinity) = 1/2

Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.

[Lost User]

Curious and grandi'ous at the same time

[Kyle Moyer]

If I remember correctly, it has something to do with the way that sums/series work when dealing with infinities. I don't remember exactly how it reduces, but I remember my mind being moderately blown the first time it was explained to me. Now, my attempt, as I think about right now, would be to reduce it to an infinite series of the sum of one minus one: (1 - 1) + (1 - 1) + (1 - 1) + .... Which would of course reduce to 0 + 0 + 0 + ... = 0... I know this is wrong (because I've not correctly applied whatever rule leads to the 1/2 answer,) but from a straightforward idiot's logic approach, it makes sense.

[Jon McKee]

Let S = 1 - 1 + 1 - 1 + 1..., then 1 - S = 1 - (1 - 1 + 1 - 1 + 1...). This simplifies to 1 - S = 1 - 1 + 1 - 1 + 1.... This means 1 - S = S which is simplified to 1 = 2S and finally S = 1/2.

[Richard Deeming]

The traditional - and entirely wrong :) - approach is:

G = 1 -  1 + 1 - 1 + ...

1 - G = 1 - (1 - 1 + 1 - 1 + ...)
= 1 - 1 + 1 - 1 + 1 - ...
= G
1 = 2G
1 / 2 = G

The correct answer is that the series doesn't have a sum in any meaningful sense. Or, for the quantum-minded, the sum is both 0 and 1 at the same time. :cool:

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"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

[Yusuf]

Couple weeks ago I was discussing zeta functions with my son who is senior in high school (math wiz ;) )

1 + 2 + 3 + 4 + ... = −1/12.

[Zeta function regularization - Wikipedia](https://en.wikipedia.org/wiki/Zeta\_function\_regularization) As for the original question, it is called divergent series, [Divergent series - Wikipedia](https://en.wikipedia.org/wiki/1\_%2B\_1\_%2B\_1\_%2B\_1\_%2B\_⋯)

Yusuf May I help you?

[Richard Deeming]

Yusuf wrote:

1 + 2 + 3 + 4 + ... = −1/12

That solution involves Grandi's series quite heavily: :) Ramanujan: Making sense of 1+2+3+... = -1/12 and Co. - YouTube[^]

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"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer

[Bassam Abdul Baki]

Or S = (1 - 1) + (1 - 1) + ... = 0 S = 1 - (1 - 1) - (1 - 1) - ... = 1 2S = 1 S = 1/2

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