# Math Help - Series test

1. ## Series test

Which test do I use for this series to see if it converges?

$\sum_{n=1}^{\infty}\frac{n!}{1*3*5...(2n-1)}$

Thanks

2. Originally Posted by JJ007
Which test do I use for this series to see if it converges?

$\sum_{n=1}^{\infty}\frac{n!}{1*3*5...(2n-1)}$

Thanks

$\frac{n!}{1\cdot 3\cdot 5\cdot\ldots\cdot (2n-1)}=\frac{n!(2\cdot 4\cdot 6\cdot \ldots \cdot 2n)}{1\cdot 2\cdot 3\cdot 4\cdot \ldots\cdot (2n-1)(2n)}=\frac{2^n(n!)^2}{(2n)!}$

Now you can use D'Alembert's test (= quotient test) to check it does converge.

Tonio