Re: Expressions with ellipsis (...)

*To*: mathgroup at smc.vnet.net*Subject*: [mg93015] Re: Expressions with ellipsis (...)*From*: "David Park" <djmpark at comcast.net>*Date*: Fri, 24 Oct 2008 02:27:22 -0400 (EDT)*References*: <gdmsbd$jv$1@smc.vnet.net>

If I understand your question correctly you are solving the following problem: HoldForm[Sum[(n - i)^2, {i, 0, n - 1}]/n^3] % // ReleaseHold Limit[%, n -> Infinity] \!\( \*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(n - 1\)] \*SuperscriptBox[\((n - i)\), \(2\)]\)/n^3 ((1 + n) (1 + 2 n))/(6 n^2) 1/3 But you would prefer that the initial expression was an ellipsis expression in the form of the standard textbook representation. This can be done using the functionality of the Idenfinite Sequences section of the Presentation package. This is how it would be done: Needs["Presentations`Master`"] iSum[i^2, {i, n, HoldForm[n - 1], HoldForm[n - 2], , 1}]/n^3 % // iSumNormalize[tag1, {i, n, 1}] Limit[%, n -> Infinity] (n^2 + (n-1)^2 + (n-2)^2 + ... + 1)/n^3 (but in built up box form) ((1 + n) (1 + 2 n))/(6 n^2) 1/3 iSum represents an ellipsis expression where the sequence of terms represent the explicit terms you wish to display and you can have any number of ellipses, which are entered as Nulls in the sequence. iSumNormalize will convert the iSum to a regular Sum for evaluation by Mathematica. It just substitutes a normal iterator. It is also possible to operate on the terms while they are still in the ellipsis expression. There are also ellipsis expressions for Products, Tables, Sequences and expressions with arbitrary Infixes. One of the main purposes of the Presentations package is to make it easier to use Mathematica in a 'textbook mode' and to work with standard textbooks. It has over 5 MB of code and help pages, but is probably far beyond the budget of most students. -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ "dch888" <dch888 at googlemail.com> wrote in message news:gdmsbd$jv$1 at smc.vnet.net... > 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. > >