Is 1+2+3+4+... equal to -1/12? A mind-boggling proof!

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Discussion Overview

The discussion centers around the claim that the infinite series 1 + 2 + 3 + 4 + ... equals -1/12, exploring the implications for series convergence and the validity of the proof presented in a linked video. Participants express confusion regarding traditional understandings of series and divergence.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant references a video claiming that the series equals -1/12, expressing confusion about how this aligns with established principles of series convergence.
  • Another participant argues that the sum of natural numbers up to N, given by N(N+1)/2, diverges to infinity as N approaches infinity, suggesting that a sum of positive numbers cannot yield a negative result.
  • A third participant echoes the sentiment of disbelief regarding the validity of the claim made in the video.

Areas of Agreement / Disagreement

Participants generally disagree with the claim that the series equals -1/12, with multiple viewpoints expressing skepticism about the proof and its implications for series convergence.

Contextual Notes

Participants reference traditional definitions of convergence and divergence without resolving the apparent contradiction posed by the video. The discussion does not clarify the mathematical steps involved in the proof or the assumptions underlying the claim.

Who May Find This Useful

This discussion may be of interest to those exploring series convergence, mathematical proofs, or the implications of unconventional results in mathematics.

fargoth
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I've see this neat proof:
http://www.youtube.com/watch?v=E-d9...eature=iv&annotation_id=annotation_3085392237 (for some reason the youtube tag didn't work in preview...)
And now I don't see how what I've learned about series convergence is true...
I've been told that if a_n > b_n \forall n then \sum a_n > \sum b_n therefore, if \sum b_n is divergent then, \sum a_n must be too.
Also, If the partial sum diverges, the series is said to be divergent, isn't it?
And what about a_n \neq 0 for n that tends to infinity?
So many ways I could show this series diverges, yet he show it's equal to -1/12?

Where am I, or is he, wrong?
 
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I think this cannot be true. The sum of all natural numbers up to N equals (as also shown in the end of the video) ## N(N+1)/2 ##. This obviously goes to infinity as N goes to infinity. And of course there is also no way how strictly positive numbers can add up to give a negative result.
 
That's what I was saying :)
So where is he wrong?
 
And as this link was posted we can safely close the thread.
 

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