Answer
See the details below.
Work Step by Step
Since $$\sum_{n=1}^{\infty} n^{-3.2}=\sum_{n=1}^{\infty} \frac{1}{n^{3.2}}$$ then this is a p-series which converges only if $p\gt 1$. So it converges because $p=3.2\gt 1$.
We could also use the integral test to test for convergence.
