Re: summing 1/(n!) from 21 to Infinity
- To: mathgroup at smc.vnet.net
- Subject: [mg45047] Re: summing 1/(n!) from 21 to Infinity
- From: drbob at bigfoot.com (Bobby R. Treat)
- Date: Sun, 14 Dec 2003 06:22:44 -0500 (EST)
- References: <brci24$2p7$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
The negative answer is caused by loss of precision.
N[Sum[1/(n!), {n, 21, Infinity}], 30]
Bobby
Sampo Smolander <sampo.smolander+newsnspam at helsinki.fi> wrote in message news:<brci24$2p7$1 at smc.vnet.net>...
> 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)