Sunday, 29 October 2017

sequences and series - Is the sum of natural numbers equal to frac18?

I came across the following video on YouTube: Sum of all natural numbers (- 1/8).



Basically what happens is:
1+2+3+=N1+(2+3+4)+(5+6+7)+=N1+9+18+27+=N1+9(1+2+3+4+)=N1+9N=N


and therefore N=18.



This is directly in contradiction with the well-known result of 112.



What is the problem with this reasoning? Was this result discovered earlier? Is this a consequence of Riemann's Rearrangement Theorem? Thanks in advance.



This was a repost of my previous post because some people said it was a duplicate to "Why is the sum of natural numbers 1/12?"

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