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MathGroup Archive 2008

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Re: Expressions with ellipsis (...)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93045] Re: Expressions with ellipsis (...)
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 24 Oct 2008 02:33:05 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <gdmsbd$jv$1@smc.vnet.net>

dch888 wrote:

> 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?

One cannot write a sum with ellipsis and ask Mathematica to compute it. 
One must use *Sum* (sigma notation) in this case. Here is an example:

     Limit[Sum[(n - k)^2, {k, 0, n - 1}]/n^3, n -> Infinity]

(Of course, one must first be able to find the general term of the sum.)

Regards,
-- Jean-Marc



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