Convergence of $\sum\limits_{n=0}^{\infty}\frac{n^3+n^4}{2^{n+1}}$ Does $\sum\limits_{n=0}^{\infty}\frac{n^3+n^4}{2^{n+1}}$ converges (absolute)?
I've already tried the Ratio test and the Root test test, but they failed both...

HINT, Root Test:
\begin{equation}
\lim_{n\rightarrow\infty} \sqrt[n]{\frac{n^3+n^4}{2^{n+1}}}
\end{equation}
and
\begin{equation}
\frac{n^3+n^4}{2^{n+1}}\sim \frac{n^4}{2^{n+1}}
\end{equation}
\begin{equation}
\lim_{n\rightarrow\infty} \sqrt[n]{\frac{n^4}{2^{n+1}}}=1/2<1
\end{equation}
with $\lim_{n\rightarrow\infty}\sqrt[n]n=1$
