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Recently there's been a lot of buzz created by this video http://www.youtube.com/watch?v=w-I6XTVZXww which states and goes on to prove

$$1 + 2 + 3 + ... = -\frac{1}{12} $$

I know that the above series is actually $\zeta(-1)$ where $\zeta$ is the Riemann zeta function. For someone who is not much into higher and advanced mathematics, what meaning does this equation hold? The video explain that this is a very useful result used in string theory in Physics and the basic premise which is used to prove it is

$$1-1+1-1+... = \frac{1}{2} $$ which doesn't seem quite right and which, in fact, leads to contradictions as explained here on Quora http://www.quora.com/Mathematics/Theoretically-speaking-how-can-the-sum-of-all-positive-integers-be-1-12/answer/David-Joyce-11. So, my question is is the proof shown in the video meaningless and only serve the purpose of sensationalizing by wrongly interpreting and misrepresenting mathematical results?

ajay
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    This question is frequently asked by some users in this site. Did you do the quick search? – NasuSama Jan 18 '14 at 16:18
  • Yes I did but couldn't find a similar question. Please give the link and I will delete my question. – ajay Jan 18 '14 at 16:20
  • I know what this equation means. See the end part of my question. It isn't exactly the same, though the title is the same. – ajay Jan 18 '14 at 16:28
  • The interesting part of the mentioned video is NOT the derivation, but is in the beginning of the video. It shew that a book has in fact included the quoted claim. It is a bit disappointed of not knowing (1) what that book is; (2) why is it included; (3) how the claimed result can be applied. – Mick Jan 18 '14 at 18:01

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