Does the series $\displaystyle\sum_{n=1}^{\infty} \dfrac{19+(n+5)!}{(n+7)!}$ Converge or diverge
I tried using the ratio test, but it gave me this which I don't see how you'd be able to solve. $$\lim_{n\to\infty} |\frac{a_{n+1}}{a_{n}}| = \lim_{n\to\infty}\frac{19+(n+6)!}{19+(n+5)!*(n+8)}$$
Wolfram alpha told me to use the comparison test, but I can't for the love of god see which series I'd compare it to.