# Math Help - Interval of Convergence for a Power Serires

1. ## Interval of Convergence for a Power Serires

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

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

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

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

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

2. I think your (2n+3) should be (2n+1), shouldn't it? There are n terms in the multiplication of odd numbers in the denominator of the nth element of the series. Otherwise, it looks fine to me.

3. Yes, that's right. I checked it.