I need to find $\lim_{n \to \infty}$ $(1 + \frac{3}{n^2})^{n^2}$ and I've been given the following:
$\lim_{n \to \infty}$ $n^{1/n}$ = 1, $\lim_{n \to \infty}$ $a^{1/n}$ = 1 and $\lim_{n \to \infty}$ $(1 + \frac{1}{n})^{n}$ = e.
My first thoughts were to use the 3rd limit so $(1 + \frac{3}{n^2})^{n^2}$ <= 3e$^{n}$ and then using the squeeze theorem to show as n tends to infinity the sequence is null, but I think I'm missing something out.