calculus - $lim_{nto infty} n^3(frac{3}{4})^n$

I have the sequence $a_n=(n^3)\big(\frac{3}{4}\big)^n$

and I need to find whether it converges or not and the limit.

I took the common ratio which is $\frac{3 (n+1)^3}{4 n^3}$ and since $\big|\frac{3}{4}\big|<1$ it converges.
I don't know how to find the limit from here.

Answer

If $\frac {a_{n+1}} {a_n} \to l$ with $|l|<1$ then $a_n \to 0$. (In fact the series $\sum a_n$ converges).

In this case $\frac {a_{n+1}} {a_n} =(1+\frac 1 n)^{3}(\frac 3 4) \to \frac 3 4$.