Does $n^{1000000}/2^{n}$ converge as $n\rightarrow+\infty$?

To solve this problem, I am only allowed to use elementary properties of limits. This is what I tried. For $n > 1000000$, one has that
\begin{align\*}
\frac{n^{1000000}}{2^{n}} = \left(\frac{n}{2}\right)^{1000000}\times\left(\frac{1}{2}\right)^{n-1000000}
\end{align\*}

But then I get stuck. This is not homework. Could someone help me out?