$a_n=\frac{c^n(n^2+3n+5)}{5^n(4n^n+3n+5)}$ where $c$ is a real constant Find the limit as $n \to \infty$ of this series.
I’ve used the ratio test and written it in the form $\frac {a_{n+1}}{a_n} $ Which gives me $\frac{c(n^2+5n+7)(4n^2+3n+5)}{5(16n^2+35n+9) (n^2+3n+5)}$ I don’t know what to do after this. Should I multiply the brackets or is there an easier way to find the limit?