# Thread: Sum of convergent series

1. ## Sum of convergent series

Ok, so here is my problem:

Find the sum of the convergent series:

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

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!

Ok, so here is my problem:

Find the sum of the convergent series:

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

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 ?

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

3. Well, that function represents the sin(x) but I'm really not sure where the 3^(2n+1) comes in at all.

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