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Re: summing 1/(n!) from 21 to Infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45015] Re: [mg44998] summing 1/(n!) from 21 to Infinity
  • From: Richard Gass <gass at physics.uc.edu>
  • Date: Sat, 13 Dec 2003 06:06:00 -0500 (EST)
  • References: <200312120941.EAA24153@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

What version of Mathematica are you using. I get

In[8]:=
test=E - E Gamma[m,1]/Gamma[m]

Out[8]=
     E Gamma[m, 1]
E - -------------
       Gamma[m]

In[9]:=
In[1]:=
test=E - E Gamma[m,1]/Gamma[m]

 From In[1]:=
E - (E*Gamma[m, 1])/Gamma[m]

Out[1]=


In[2]:=
N[test/.m->21,30]

 From In[2]:=
2.05029806862466116108436591596978541904158375453`30.*^-20

Out[2]=


In[3]:=
N[Sum[ 1 /(n!), {n, 21, Infinity}] ,30]

 From In[3]:=
2.05029806862466116108436591596978541904158375453`30.*^-20

Out[3]=
Both results are correct.  Notice however, that all the results 
(including yours) are zero to which machine precision.

On Dec 12, 2003, at 4:41 AM, Sampo Smolander wrote:

> 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"
>
>
>


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