Re: summing 1/(n!) from 21 to Infinity
- To: mathgroup at smc.vnet.net
- Subject: [mg45020] Re: summing 1/(n!) from 21 to Infinity
- From: Sampo Smolander <sampo.smolander+newsnspam at helsinki.fi>
- Date: Sat, 13 Dec 2003 06:06:06 -0500 (EST)
- Organization: University of Helsinki
- References: <brci24$2p7$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Sampo Smolander <sampo.smolander+newsnspam at helsinki.fi> wrote:
> 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]
I got it:
This the thing they teach first in the most basic numerical analysis
courses. Since E and E Gamma[m,1]/Gamma[m] (with m>20) are very close each
other, the result of this subtraction is mostly the rubbish from the
low-order bytes when the floating point precision is not good enough.
Easy to fix by increasing the precision.