Determine whether $\sum_{n=1}^{\infty} \frac{n^3}{3^n}$ converges or diverges.
$\left| \frac{a_{n+1}}{a_n} \right| = \left| \frac{\frac{(n+1)^3}{3^{n+1}}}{\frac{n^3}{3^n}} \right| = \left| \frac{(n+1)^3(3^n)}{(n^3)(3^{n+1})} \right| = \left| \frac{(n+1)^3}{3n^3} \right| $
How do I proceed from here?
