Series $\sum_{n=2}^\infty \frac{14^n}{3^{3n+4}(3n+7)}$ Convergence or Divergence Using The Ratio Test I am trying to determine if the following series converges or diverges by using the ratio test, which I believe can be summarized as the following:
$$L=\lim_{n\to \infty}  \left| \frac{a_{n+1}}{a_n} \right|$$
If $L < 1$ then the series converges, if $L > 1$, then it diverges, and if $L = 1$, then it is ambiguous. The series is below:
$$\sum_{n=2}^\infty \frac{14^n}{3^{3n+4}(3n+7)}$$
I understand the ratio test in theory, but am not sure how to put it into practice for a series like this.

Here we have
$$a_n=\dfrac{14^n}{3^{3n+4}(3n+7)}$$
so that
$$a_{n+1}=\dfrac{14^{n+1}}{3^{3(n+1)+4}(3(n+1)+7)}=\dfrac{14\cdot 14^n}{3^{3n+4}\cdot 3^3(3n+10)}$$
Try to compute the limit of $a_{n+1}/a_n$ as $n\rightarrow\infty$.
