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