Re: summing 1/(n!) from 21 to Infinity
- To: mathgroup at smc.vnet.net
- Subject: [mg45033] Re: summing 1/(n!) from 21 to Infinity
- From: bobhanlon at aol.com (Bob Hanlon)
- Date: Sat, 13 Dec 2003 06:06:36 -0500 (EST)
- References: <brci24$2p7$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
The result is smaller than your machine precision so your result is
meaningless. Increase your precision.
N[Sum[1/(n!),{n,21,Infinity}],25]
2.050298068624661161084365915969785418970795`25*^-20
Sum[1/(n!),{n,m,Infinity}]
E - (E*Gamma[m, 1])/Gamma[m]
N[%/.m->21, 25]
2.050298068624661161084365915969785418970795`25*^-20
Bob Hanlon
In article <brci24$2p7$1 at smc.vnet.net>, Sampo Smolander
<sampo.smolander+newsnspam at helsinki.fi> 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)