From the listed choices, you can prove the series diverges using either the integral or p-series test.
We have
[tex]\displaystyle\sum_{n=1}^\infty\ge\int_1^\infty\frac{\mathrm dx}{\sqrt x}=\lim_{x\to\infty}2\sqrt x-2[/tex]
which diverges to infinity, so the series is divergent.
The series
[tex]\displaystyle\sum_{n=1}^\infty\frac1{n^p}[/tex]
converges only for [tex]p>1[/tex]. In the given sum, we have [tex]p=\frac12<1[/tex], so the series is divergent.
