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

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ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink] New post 31 Jan 2014, 00:41
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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] New post 31 Jan 2014, 11:49
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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] New post 31 Jan 2014, 12:32
Mind blown!! :D

Thanks for sharing.
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink] New post 31 Jan 2014, 14:22
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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] New post 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] New post 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] New post 02 Feb 2014, 01:27
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ... [#permalink] New post 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] New post 10 Feb 2014, 08:42
It gave me a headhache trying to understand... This is really complex... :)
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Re: ASTOUNDING!!! What is 1 + 2 + 3 +4 + ...   [#permalink] 10 Feb 2014, 08:42
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ASTOUNDING!!! What is 1 + 2 + 3 +4 + ...

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