Re: Expressions with ellipsis (...)

*To*: mathgroup at smc.vnet.net*Subject*: [mg93017] Re: [mg92995] Expressions with ellipsis (...)*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Fri, 24 Oct 2008 02:27:45 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200810220939.FAA00651@smc.vnet.net>*Reply-to*: murray at math.umass.edu

If you just want to evaluate this, then it's easy since, among other things, there's a well-know closed-form expression for the sum of squares of the first n positive integers: Sum[(n - i)^2, {i, 0, n - 1}] (n*(1 + n)*(1 + 2*n))/6 (I'm showing InputForm for the output here rather than the usual OutputForm that would show fractions build up in 2 dimensions.) And so: Limit[%/n^3,n->Infinity] 1/3 Or, of course, the whole thing together: Limit[Sum[(n - i)^2, {i, 0, n - 1}]/n^3, n->Infinity] 1/3 If you want to DISPLAY such an "indefinite sum", then David Park's "Presentations" application package helps: Needs["Presentations`Master`"] iSum[(n - i)^2, {i, 0, 1, 2, , n - 1}] n^2 + (-1+n)^2 + (-2+n)^2 + ... + 1 (literally just like that, except that the exponents are shown as superscripts). dch888 wrote: > Hi Mathematica Friends, > > I want to do this: > > Limit[(n^2 + (n - 1)^2 + (n - 2)^2 + ... + 1)/n^3, n -> Infinity] > > But Mathematica barfs: > > expression cannot be followed by "...". > > Searching the help for 'ellipsis' gives me the Unicode 2026 character > (i.e. ...). > > How can I get Mathematica to eval this limit? > > Thanks, > David. > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Expressions with ellipsis (...)***From:*dch888 <dch888@googlemail.com>