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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




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