a is the real number ,Studen the convergence of the sequence :
$\displaystyle
U_{n}=\frac{a^{n}}{n^{n}}
$
$\displaystyle U_n = \left( \frac{a}{n} \right)^n$
You said sequence, not series, so this question is about the behavior of U_n as n approaches infinity. I would start with assuming $\displaystyle \lim_{n \rightarrow \infty} U_n = L$ and play around with that, most likely using logarithms.