The series converges by direct comparison

We can compare because $\frac{1}{n^2+n} < \frac{1}{n^2}$ for all $n \geq 1$, and $\sum \frac{1}{n^2}$ converges

The series diverges by direct comparison

We can compare because $\frac{1}{n^2+n} > \frac{1}{n^2}$ for all $n \geq 1$