Chapter 9.5, Problem 4QCE

Select between converges or diverges to fill the first blank.

Since $\underset{k\to +\infty }{\lim }{\left(\frac{1}{k^{k/2}}\right)}^{1/k}=\underset{k\to +\infty }{\lim }\frac{1}{k^{1/2}}=0$ the series ${\displaystyle {\sum }_{k=1}^{\infty }1/k^{k/2}}\text{\_\_\_\_\_}$ by the $\text{\_\_\_\_\_}$ test.