I need confirmation that I'm applying the ratio test correctly.

$\displaystyle \Sigma_{n=0}^{\infty}\left(\frac{n!(x-c)^n}{1\cdot 3\cdot 5\cdot\cdot\cdot (2n-1)}\right)$

$\displaystyle \lim_{n->\infty}\mid\frac{(n+1)!(x-c)^{n+1}}{1\cdot 3\cdot 5\cdot\cdot\cdot (2n-1)(2n+3)}\frac{1\cdot 3\cdot 5\cdot\cdot\cdot (2n-1)}{n!(x-c)^n}\mid $

I'm not certain if I'm setting that up correctly.

If it's correct, It should be easy from this point on.