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# ASTOUNDING!!! What is 1 + 2 + 3 +4 + ...

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ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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31 Jan 2014, 00:41
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Expert's post

Disclaimer: please do NOT apply this on the test!!! Very much out of scope!!!

What would you say is the value of 1 + 2 + 3 + 4 + 5 + ... to infinity ? I bet you'd be surprised to know it's:

[Reveal] Spoiler:
$$-\frac{1}{12}$$

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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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31 Jan 2014, 11:49
Bunuel wrote:

Disclaimer: please do NOT apply this on the test!!! Very much out of scope!!!

What would you say is the value of 1 + 2 + 3 + 4 + 5 + ... to infinity ? I bet you'd be surprised to know it's:

[Reveal] Spoiler:
$$-\frac{1}{12}$$

Bunuel,
This is great! It's funny the way those guys, physicists, talk about how the sum is "really" -1/12. Yes, that's really what it would be for Physicists, especially for String Theorists, but not at all what it would be for Mathematicians! This entire discussion really gets into some very profound areas --- the difference between the math used in Physics and the math used in pure Mathematics; the difference between operational mathematics and mathematical rigor; the deeply ambiguous nature of infinity and exactly what it means; the relationship of mathematical ideas to the physical world; etc. It think most students here would not appreciate that mathematics, far from being a totally cut-and-dry unambiguous field, is at higher levels very much a matter of multiple possibilities governed by convention and tastes. All this is well beyond the GMAT or anything particularly relevant to the business world, but it certainly is fascinating.
Thanks for posting this.
Mike
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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31 Jan 2014, 12:32
Mind blown!! :D

Thanks for sharing.
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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31 Jan 2014, 14:22
So next time the bank calls me for the loan, I can just show them this video and give 8 cents? Or rather inform them that they owe me 8 cents to be exact... that will teach them!
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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01 Feb 2014, 12:06
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Wooow.... Am I glad that I decided against becoming a physicist... Else wouldn't have got past the first chapter of the book...
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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01 Feb 2014, 13:13
This is amazing Bunuel! Love this kind of stuff. Do you have more of these videos?
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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02 Feb 2014, 01:27
JackDaniels wrote:
This is amazing Bunuel! Love this kind of stuff. Do you have more of these videos?

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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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02 Feb 2014, 09:31
There is one little thing I do not fully understand in this equation. When he is calculating 2S(2), he shifts the second row a bit. On what ground is he allowed to do that?
I am probably missing something stupid ..
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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10 Feb 2014, 08:42
It gave me a headhache trying to understand... This is really complex...
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ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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14 Jan 2015, 01:59
Bunuel wrote:

Disclaimer: please do NOT apply this on the test!!! Very much out of scope!!!

What would you say is the value of 1 + 2 + 3 + 4 + 5 + ... to infinity ? I bet you'd be surprised to know it's:

[Reveal] Spoiler:
$$-\frac{1}{12}$$

Why -1/12 is a gold nugget: https://www.youtube.com/watch?v=0Oazb7IWzbA by Professor Edward Frenkel
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink]

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14 Jan 2015, 07:14
Just have an observation;

If you take the numbers they are taking, [1, 2, 3, 4], than 2S2 ==> 1 -2 + 1 + 3 - 2 - 4 + 3 - 4 This is exactly what they are saying in the video.

The result of this is not 1/4,as you can see but - 4. BUT they are using infinity. Therefore, here is where I got confuse. Since they are moving aside the second serie (to get the 1 - 1 + 1 ... ), it also shift the last number no? Therefore the last number must be moved aside too.

Example: if you go until 10, then your serie will be -10. And so forth until infinity. If the serie will go until 1, then the result will be 11.

In consequence, the last number is either + or - infinity.

S2 = + or - infinity.

Then, we know that S - S2 = 4S

So S = -S2/3

If S2 = + infinity then the result is negative and will not have any sense.

But if S2 = - infinity than S = + infinity, which make a bit more sense!

Thanks for this video again!
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ...   [#permalink] 14 Jan 2015, 07:14
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