(i) (1-1/n)^n I have found that the limit is 1/e but cannot show why

(ii) (1 + 1/n)^(n^2) I figure that this have something to do with e being the limit of (1 + 1/n)^n but cant see how to proceed

(iii) (1 + 1/(n^2))^n

(iv) Sqrt(n^2 + 2*n) - n

Thanks in advance for any help you can provide