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From: "Randy Brukardt" <randy@rrsoftware.com>
Newsgroups: comp.lang.ada
Subject: Re: Numerical calculations: Why not use fixed point types for
 everything?
Date: Thu, 7 Feb 2013 21:17:10 -0600
Organization: Jacob Sparre Andersen Research & Innovation
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Date: 2013-02-07T21:17:10-06:00
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"Shark8" <onewingedshark@gmail.com> wrote in message 
news:2414e19f-1d1c-4fb4-b727-76437ef099f7@googlegroups.com...
> Nicely explained, Randy.
>
> The sum formula is either n*(n-1)/2 or n*(n+1)/2, I forget which.

Yup. I think which one is right depends on whether you start counting at 0 
(in that case, it's the right-hand one) or at 1.

It stuck me this morning that you can't do a transformation like this in the 
case of power series (like a Taylor series); I don't want to appear to be 
claiming that this can ALWAYS be done, but in most cases it can be done. And 
executing a handful of operations rather than hundreds is going to be faster 
and probably more accurate.

                                 Randy.