Indeterminate Forms: Converging to e & 1

[JG89]

I know \lim_{n \rightarrow \infty} (1 + 1/n)^n = \lim_{n \rightarrow \infty} 1^{\infty}, which is an indeterminate form, converging to e in this case. But what if the original sequence is a_n = 1^n. Then as n tends to infinity, the function converges to 1 (because it's constant and the limit of a constant function is any term of the sequence). Is my reasoning correct here?EDIT: The original sequence is (1 + 1/n)^n, I messed up my latex.

 

[arildno]

Yes, you are correct.