Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.I was never very good at limits. I know that the limit of $\displaystyle \left(1 + \frac{1}{n}\right)^n$ as n goes to infinity is e, but only because they made us memorize it. I don't understand why that is, or how to use it to solve this problem. About the only technique I know you can use is the squeeze theorem, but I never understood how to come up with the two squeezing functions. Could someone explain how to do this problem?

$\displaystyle a_n = \left(1 + \frac{1}{n^2}\right)^n$

Thank you!