# How do you determine if a_n = (1+1/n^2)^n converge and find the limits when they exist?

${\lim}_{n \to \infty} {a}_{n} = 1$
${a}_{n} = {\left(1 + \frac{1}{n} ^ 2\right)}^{n} = {\left({\left(1 + \frac{1}{n} ^ 2\right)}^{{n}^{2}}\right)}^{\frac{1}{n}}$
${\lim}_{n \to \infty} {a}_{n} \approx {\lim}_{n \to \infty} {e}^{\frac{1}{n}} = 1$ and the sequence ${a}_{n}$ converges.