real analysis - Convergence of $displaystylelim_{ntoinfty}(a_n)^n$

What can we say about $\displaystyle\lim_{n\to\infty}(a_n)^n$ given a real sequence $(a_n)$? In particular what happens when $(a_n)$ is convergent? Is it possible for the described limit to converge if $(a_n)$ is not convergent?