In article
<160314c7-bf07-4d47-8e45-501bc8dd1959@[EMAIL PROTECTED]
>,
Vladimir Bondarenko <vb@[EMAIL PROTECTED]
> wrote:
>NSum[(Cos[n]/n)^1, {n, 1, Infinity}] slow convergence
>NSum[(Cos[n]/n)^2, {n, 1, Infinity}] fast convergence
>0.0420195 RIGHT
>0.572578 WRONG
>Any comments?
The convergence in the first is very slow, but
one can give the precise solution, and it is
quite possible that Mathematica recognizes the
conversion to logarithmic series.
For the second, the convergence is slow, and
Mathematica might not reccgnize that the expression
can be computed using polylogarithms.
So the success was because the first expression
with the argument of the cosine being nx is
analytically simpler than the second with the
same thing done.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
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