Sum of convergent series

• April 25th 2010, 05:18 PM
Sum of convergent series
Ok, so here is my problem:

Find the sum of the convergent series:

$\sum_{n=0}^{\infty }\frac{(-1)^n\pi ^{2n+1}}{3^{2n+1}(2n+1)!}$

Im wondering if someone can push me in the right direction of this.. Do I find partials sums and then find an nth term from those partial sums? Help on this would be much appreciated!
• April 25th 2010, 05:28 PM
skeeter
Quote:

Ok, so here is my problem:

Find the sum of the convergent series:

$\sum_{n=0}^{\infty }\frac{(-1)^n\pi ^{2n+1}}{3^{2n+1}(2n+1)!}$

Im wondering if someone can push me in the right direction of this.. Do I find partials sums and then find an nth term from those partial sums? Help on this would be much appreciated!

hint ... what function does this series represent ?

$\sum_{n=0}^{\infty }\frac{(-1)^n x^{2n+1}}{(2n+1)!}$
• April 25th 2010, 05:32 PM
Well, that function represents the sin(x) but I'm really not sure where the 3^(2n+1) comes in at all.
• April 25th 2010, 05:42 PM
skeeter
Quote:

$x^{2n+1} = \left(\frac{\pi}{3}\right)^{2n+1}$