I understand how to do all of this, but I have a question about one part:

Find the radius of convergence and the interval of convergence for:

$\displaystyle \sum^{\infty}_{n=1} \frac{n!x^n}{7\cdot 15 \cdot 23 \cdot ... (8n -1)}$

Did the ratio test:

$\displaystyle \lim_{n \rightarrow \infty} |x| \frac{n+1}{8n+7}$

***Here is where I am confused...what happens to this when I take this limit?

I think it is:

$\displaystyle \lim_{n \rightarrow \infty} |x| \frac{n+1}{8n+7}$ = $\displaystyle |x| \frac{1}{8} $

but I'm not sure, and I don't really understand why it would or would not be

$\displaystyle \frac{1}{8}$

...How do I evaluate this part and can someone show me the process? Thanks!!

****NEVERMIND!!!! I see it!