Re: Unknown Sum of Series
- To: mathgroup at smc.vnet.net
- Subject: [mg63670] Re: Unknown Sum of Series
- From: Peter Pein <petsie at dordos.net>
- Date: Mon, 9 Jan 2006 04:49:12 -0500 (EST)
- References: <dpb3vu$9tg$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Klaus G. schrieb:
> Mathematica 5.0 is not able to compute the symbolic sum:
>
> Sum[(-1)^(1 + n)*(E - ( 1 + (1/n))^n ), {n, 1, Infinity}]
>
> However, Nsum[...] results in 0.4456224031968407..
>
> I tried http://oldweb.cecm.sfu.ca/projects/ISC/ to find hidden
> constants in that number like Pi or E, but without success.
>
> Any idea?
>
> Klaus G.
>
According to http://mathworld.wolfram.com/AlternatingSeries.html there is
(apparently(!)) no closed form known.