Andrey,
in this case the value of the "limit" is highly dependent on the chosen
approximation
07.06.2012 21:00, Andrey G. Grozin ?????:
> On Thu, 7 Jun 2012, Evgeniy Maevskiy wrote:
>> You mean not SERIES, bat SEQUENCE.
>>
>> The problem is not correct from a mathematical point of view. See the
>> mathematical definition of LIMIT.
> This is a reply from a pure mathematician :-)
>
>> From the point of view of physics (or other applied sciences), the
> question is absolutely meaningful. And people do this sort of things often.
>
> It would be useful to have some theoretical guesses about how this
> sequence converges to a limit - exponentially, by a power law, or
> something. If, for example, we suppose a power-law convergence, then a
> reasonable procedure is to use the anzatz
>
> x_n = c_0 + c_1/n + c_2/n^2 + ...
>
> and fit the coefficients c_0, c_1, ... to the data (probably, omitting
> an initial part of the sequence where this asymptotics is not yet
> valid). Then c_0 is the limit.
>
> Another often situation is exponential:
>
> x_n = c_0 + c_1 \exp(-a_1 n) + c_2 \exp(-a_2 n) + ...
>
> (for example, x_n is an activity of a sample with several isotopes with
> different life times). Again, fit the data, and you have the limit
> (perhaps, the percentage of uranium, which has nearly infinite life time).
>
> If you know nothing about your sequence, just try a few models and
> choose the one which fits the data best.
>
> Andrey