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Re: error with Sum and Infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102472] Re: error with Sum and Infinity
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Mon, 10 Aug 2009 04:16:36 -0400 (EDT)

On 8/9/09 at 6:19 PM, fateman at cs.berkeley.edu (Richard Fateman)
wrote:

>You and I know that Mathematica didn't do the right thing. But there
>was no way for a user to determine if the problem was ill-posed in
>terms of Mathematica.

I disagree. The problem posed was an infinite sum of terms all 0
except at for one term with a value of 1. Any real thought about
the posed problem should come to the clear conclusion
Mathematica cannot literally sum an infinite series. For an
arbitrary series, it would seem the apparent the most direct way
to evaluate such a sum would be to sample various terms. Such an
approach with the specific series should lead one to expect the
result 0. It seems to me for problems of this sort, there is a
lack of thinking about what is known and drawing reasonable
conclusions from that.




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