Can someone check to see if I evaluated this correctly?
$\displaystyle \sum^{\infty}_{n+1} \frac{n!x^n}{8\cdot 17\cdot 26\cdot ...(9n-1)}$
$\displaystyle = \sum^{\infty}_{n+1} \frac{n!x^n}{(9n-1)!}$
Is that right?
if that's the case, why not use the ratio or root test? you don't need to rewrite anything. probably the ratio test will be easier here
however, in general, you can use Stirling's approximation.