Answer
Convergent
Work Step by Step
Given $$\sum_{n=1}^{\infty} \frac{\arctan n}{n^{1.2}}$$
Since
$$ \frac{\arctan n}{n^{1.2}}< \frac{\pi/2}{n^{1.2}} $$
for all $n\geq 1$ , then compare with the convergent series $\displaystyle\frac{\pi}{2} \sum_{n=1}^{\infty} \frac{1}{n^{1.2}}$ because $ p=1.2>1$, hence $$\sum_{n=1}^{\infty} \frac{\arctan n}{n^{1.2}}$$
is also convergent.