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Re: How to show 1+2+3+ ... = -1/12 using Mathematica's symbols?

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  • Subject: [mg132225] Re: How to show 1+2+3+ ... = -1/12 using Mathematica's symbols?
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Mon, 20 Jan 2014 04:00:45 -0500 (EST)
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On 1/18/2014 11:52 PM, Matthias Bode wrote:
> Hola,
>
> I came across this video (supported by the Mathematical Sciences Research Institute* in Berkeley, California):
>
> http://www.numberphile.com/videos/analytical_continuation1.html
>
> Could the method shown in this video be replicated using Mathematica symbols such as Sum[] &c.?
>
> Best regards,
>
> MATTHIAS BODES 17.36398=B0, W 66.21816=B0,2'590 m. AMSL.
>
> *) http://www.msri.org/web/msri
>

Sure. Piece of cake.
Sum[a^n,{n,0,Infinity}]   results in  1/(1-a).

%/. a->-1  tells you that this Sum is 1/2

Starting from this lie  (the sum is actually divergent), you should
be able to prove lots and lots of things.






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