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