(Xn) = (1 + 1/n^2)^n^2

i) does it converge?

ii) find the limit.

attempt at a solution for i):

- prove that it is monotonic and bounded

=> convergence

- bounded:

|(Xn)| <= M , all n in Naturals

(1 + 1/n^2)^n^2 <= M

n^2ln((n^2 + 1)/n^2) <= lnM

n^2ln(n^2 + 1)-n^2ln(n^2) <= lnM

n^2ln(n^2 + 1)-n^2ln(n^2) <= n^2ln(n^2 + 1) so,

n^2ln(n^2 + 1) <= lnM

not sure how to continue...

ii) have yet to try

thanks