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"
>
>
>
- References:
- summing 1/(n!) from 21 to Infinity
- From: Sampo Smolander <sampo.smolander+newsnspam@helsinki.fi>
- summing 1/(n!) from 21 to Infinity