Chapter 9.5, Problem 3QCE

Select between converges or diverges to fill the first blank.

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