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.