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summing 1/(n!) from 21 to Infinity

• To: mathgroup at smc.vnet.net
• Subject: [mg44998] summing 1/(n!) from 21 to Infinity
• From: Sampo Smolander <sampo.smolander+newsnspam at helsinki.fi>
• Date: Fri, 12 Dec 2003 04:41:57 -0500 (EST)
• Organization: University of Helsinki
• Sender: owner-wri-mathgroup at wolfram.com

I'd be happy if somebody explained what could be behind
this odd behavior:

When I do:

   Sum[ 1 /(n!), {n, 21, Infinity}] // N

I get a -4.44089 * 10^(-16), which doesn't make much
sense, since it's negative and none of the summands are.

The same with symbolic starting point,

   Sum[ 1 /(n!), {n, m, Infinity}] // N

gives:

   E - E Gamma[m,1]/Gamma[m]

Now where might the mistake be? I don't know enough maths to be able to
say whether the symbolic sum is wrong -- which however feels more likely
than a mistake in the implementation of the gamma function.

(I computed the above with Mathematica 4.0, on win98)

-- 
Sampo Smolander at Helsinki Fi.......http://www.rni.helsinki.fi/~shs/
"Because, no matter what you do, everything comes down to one of two  
things: biology or math." Stephen Franklin in Babylon 5: "Exogenesis"

• Follow-Ups:
  • Re: summing 1/(n!) from 21 to Infinity
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: summing 1/(n!) from 21 to Infinity
    • From: Richard Gass <gass@physics.uc.edu>