Limits of Sequences

A startup's growth factor after $n$ months is modeled by $a_n = \sqrt[n]{n}$. What value does this growth factor approach as $n$ becomes very large?

Consider the sequence $a_n = \frac{(n!)^{1/n}}{n}$. Find $\lim_{n \to \infty} a_n$.

A biologist models the number of bacteria in a culture after $n$ hours using the expression $a_n = \sqrt{4n^2 + 2n + 1} - 2n$. As $n$ becomes very large, what value does $a_n$ approach?