Re: Unknown Sum of Series
- To: mathgroup at smc.vnet.net
- Subject: [mg63523] Re: [mg63473] Unknown Sum of Series
- From: Pratik Desai <pdesai1 at umbc.edu>
- Date: Tue, 3 Jan 2006 01:26:47 -0500 (EST)
- References: <200601021049.FAA01328@smc.vnet.net> <43B9373E.2060302@umbc.edu>
- Sender: owner-wri-mathgroup at wolfram.com
Pratik Desai wrote:
> Klaus G. wrote:
>
>> 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.
>>
>>
>>
> I tried Limit on your expression and it gives me zero,
> Limit[(-1)^(1 + n)*(E - (1 + (1/n))^n), n -> â??, Direction -> -1]
> >>0
>
> Hope this helps
>
> Pratik
>
This is obviously not going to help you much ( :-[ keep forgetting
limit works for sequences as well)
Perhaps this might be more appropriate
<< NumericalMath`NLimit`
expr1[n_] = (-1)^(1 + n)*(E - (1 + (1/n))^n) // Total
NLimit[expr1[n], n -> â??] // Chop
>>-0.999996
Hope...uh well you get the idea
Pratik
- References:
- Unknown Sum of Series
- From: "Klaus G." <Karl_boehme_9@msn.com>
- Unknown Sum of Series