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Re: Expressions with ellipsis (...)

If I understand your question correctly you are solving the following 

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)

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:


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)

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 

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

"dch888" <dch888 at> wrote in message 
news:gdmsbd$jv$1 at
> 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.

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