Chapter 9.5, Problem 2QCE

Select between converges or diverges to fill the first blank

Since $\underset{k\to +\infty }{\lim }\frac{{\left(k+1\right)}^3/3^k{}^{+1}}{k^3/3^k}=\underset{k\to +\infty }{\lim }\frac{{\left(1+\frac{1}{k}\right)}^3}{3}=\frac{1}{3}$ the series ${\displaystyle {\sum }_{k=1}^{\infty }{k}^3/3^k\text{\_\_\_\_\_}}$ by the $\text{\_\_\_\_\_}$ test.