Question

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

Answer 1

`lim_(n->oo)a_n = 1`

Explanation:

`a_n = (1+1/n^2)^n = ((1+1/n^2)^(n^2))^(1/n)`

and then

`lim_(n->oo) a_n approx lim_(n->oo) e^(1/n) = 1` and the sequence `a_n` converges.