Re: summing 1/(n!) from 21 to Infinity
- To: mathgroup at smc.vnet.net
- Subject: [mg45034] Re: summing 1/(n!) from 21 to Infinity
- From: Bill Rowe <readnewsciv at earthlink.net>
- Date: Sat, 13 Dec 2003 06:06:40 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On 12/12/03 at 4:41 AM, sampo.smolander+newsnspam at helsinki.fi (Sampo Smolander) 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.
Look at the magnitude of this result. You've asked Mathematica to give a machine precision approximation for the result. You should expect Mathematica to give you something either a bit smaller or a bit larger than the true result when you do this. The fact the summands are positive and you got a small negative value indicates the true result is likely to be very nearly 0.
> 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?
There is no mistake. Here you've asked Mathematica to give you a symbolic result, which it did. Asking for a numeric approximation does nothing since you've not assigned numberic values to any of the symbols
If you do
(E - E Gamma[m,1]/Gamma[m]/.m->21)//N
You should get the same result as when you did
Sum[ 1 /(n!), {n, 21, Infinity}] // N
Also note if you want a numeric answer it might be better to use NSum rather than Sum followed by N.
--
To reply via email subtract one hundred and nine