Comparison Test for Series I am trying to prove that the series below converges by the comparison test. 
\begin{align}
\sum_{n=1}^\infty\frac{2n^3+5^n+5\log(n)}{13-n+8^n}
\end{align}
How do I show that:
\begin{align}
\frac{2n^3+5^n+5\log(n)}{13-n+8^n} \le 16\left(\frac{5}{8}\right)^n
\end{align}

Note for n>1:
$$ 
\dfrac{2n^3 + 5^n + 5\log(n)}{13-n+8^n}  \leq \dfrac{2\cdot 5^n + 5^n + 5^n}{\frac{8^n}{2}} =  8\bigg( \frac{5}{8} \bigg)^n 
$$
and note that $\frac{5}{8} < 1$ so the series will converges by geometric series. 
