The sum of an infinite series

[inknit]

\sum [(-1)^n * pi ^2n] / [9^n * (2n)!] = ?

Thanks for the help.

[CompuChip]

I assume that the summation runs from n = 0 to \infty.

In that case, you might (if you have seen it often enough before) recognise that the sum looks a bit like the cosine series
\cos x = \sum_{n = 0}^\infty a_n x^n
with an = .... ?

[HallsofIvy]

\sum [(-1)^n * pi ^2n] / [9^n * (2n)!] = ?

Thanks for the help.
Write that as
\sum \frac{(-1)^n}{(2n)!}\left(\frac{\pi}{3}\right)^{2n}
and it is the Taylor's series for [itex]cos(\pi/3)[/tex]. Do you know what that is?