Disprove a convergence question

1. Dec 5, 2008

transgalactic

i know that An->1

i need to prove that (An)^n ->1

but when i construct limit
lim (An)^n
n->+infinity

the base goes to 1 and the power goes to + infinity

that is not solvable

i get 1^(+infinity) which says that there is no limit
what do i do in this case in order to disprove that (An)^n->1

??

2. Dec 5, 2008

Staff: Mentor

All you need is a counterexample to show that
$$\lim_{n \rightarrow \infty} (a_n)^n = 1$$ isn't true.

You need a sequence {a_n} whose limit is 1 but for which the limit above isn't 1.