Re: How to show 1+2+3+ ... = -1/12 using Mathematica's symbols?
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- Subject: [mg132228] 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 04:01:45 -0500 (EST)
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On 1/19/2014 8:02 AM, Richard Fateman wrote: > 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. > > > Oh, I should point out that if you are clever enough and want to avoid this, you could type Sum[a^n,{n,0,Infinity}, GenerateConditions-> True] which returns ConditionalExpression[1/(1 - a), Abs[a] < 1] RJF