
Re: How to show 1+2+3+ ... = 1/12 using Mathematica's symbols?
Posted:
Jan 21, 2014 2:58 AM


Note that:
In[25]:= Sum[n, {n, 1, Infinity}, Regularization > "Dirichlet"]
Out[25]= (1/12)
This is of course, perfectly correct ;)
Andrzej
On 20 Jan 2014, at 10:01, Murray Eisenberg <murray@math.umass.edu> wrote:
> You may try the Regularization option for Sum, but it doesn't seem to give any finite result for that divergent series. > > On the other hand, the video to which you refer relies ultimately upon using Ces=E0rosummability of 1  1 + 1  1 _ . . . , which you may implement in Mathematica as: > > Sum[(1)^n, {n, 0, \[Infinity]}, Regularization > =93Cesaro"] > (* 1/2 *) > > [The video to which you refer is disingenuous in not saying upfront that it's not using ordinary summability but some other form(s) of summability. (The merest hint is a brief glimpse of a page of a text on String Theory where the formula > 1 + 2 + 3 + . . . = 1/12 is displayed just below a line referring to renormalization.) > > As it stands, that video, in my mind, is deleterious to understanding of the mathematics of infinite series destructive of trust in mathematics: it manipulates divergent series as if they were convergent.] > > > On Jan 19, 2014, at 2:56 AM, Matthias Bode <lvsaba@hotmail.com> 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 >> > > Murray Eisenberg murray@math.umass.edu > Mathematics & Statistics Dept. > Lederle Graduate Research Tower phone 240 2467240 (H) > University of Massachusetts > 710 North Pleasant Street > Amherst, MA 010039305 > > > > > > >

