Tell me more ×  Given is the following sequence
$a_n=(-n)^{(-n)^n}$ $(n \in \mathbb{N})$. Find all limit points.
Here's what I have so far, I divided it in three cases.  Case 1:
$-n > 0 \rightarrow n < 0$  I did this "trick" $m=-n,
a_n=m^{m^{-m}}$  $m^{-m}$ converges to $0$ and therefore, $a =
m^0 = 1$, when $n$ tends to infinity. This is our only limit
point.  Case 2: $-n < 0 \rightarrow n > 0$  I divided into two
more cases here:  n is even: $-n^n$ diverges to negative
infinity, therefore $a_n=(-n)^{(-n)^n}$ also. n is odd: $-n^n$
diverges to positive infinity, therefore $a_n=(-n)^{(-n)^n}$
also.  Is this correct? Thanks  share|improve this question Just
because $g(x)$ converges to $0$ doesn't mean that $f(x)^{g(x)}$
converges to 1. So that fact that $m^{-m}\to 0$ doesn't mean
that $m^{m^{-m}}\to 1$ –  Thomas Andrews Nov 15 '11 at 19:02
Case 2: $n$ even: $-n^n\rightarrow-\infty$; but $(-n)^n$ does
not... –  David Mitra Nov 15 '11 at 19:03 1. what is the domain
of $n$, doesn't it take only positive values?