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

*To*: mathgroup at smc.vnet.net*Subject*: [mg132233] Re: How to show 1+2+3+ ... = -1/12 using Mathematica's symbols?*From*: Andrzej Kozlowski <akozlowski at gmail.com>*Date*: Tue, 21 Jan 2014 03:02:28 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <20140119075641.AB76D69EE@smc.vnet.net> <20140120090105.33E5969EA@smc.vnet.net>

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 at 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=E0ro-summability 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 up-front 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 at 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 at math.umass.edu > Mathematics & Statistics Dept. > Lederle Graduate Research Tower phone 240 246-7240 (H) > University of Massachusetts > 710 North Pleasant Street > Amherst, MA 01003-9305 > > > > > > >

**References**:**How to show 1+2+3+ ... = -1/12 using Mathematica's symbols?***From:*Matthias Bode <lvsaba@hotmail.com>

**Re: How to show 1+2+3+ ... = -1/12 using Mathematica's symbols?***From:*Murray Eisenberg <murray@math.umass.edu>