Re: convergence of series involving arctan, arcsin or arccos.

"katy" <mcld@xxxxxxxxxxxxxxx> writes in article <1137522357.911833.126260@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> dated 17 Jan 2006 10:25:57 -0800:
>
>I'm having some problems in finding if a series is convergent or
>divergent when the geral term involves arctan, arcsin or arccos.
>
>For example,
>
> a series from n=1 to infinity with term: (3^n arcsin((-1)^n/n) )/n!
>
> Did i have to see the limit of what is inside the arcsin?

If you're using the [-pi/2,pi/2] branch of arcsin(), and you can prove that
the expression

(3^n * pi/2 )/n!

converges, you have shown that the expression with the arcsin converges.

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
.

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