Practice problem

Limit Rules for Sequences

Let two sequences $a_n$ and $b_n$ satisfy $\lim_{n \to \infty} a_n = 2$ and $\lim_{n \to \infty} b_n = 4$ . What is the value of the following limit?

\lim_{n \to \infty} \frac{a_nb_n^2}{2a_n + 3b_n}