Answer
Diverges
Work Step by Step
Consider $a_n=(\dfrac{1}{n}-\dfrac{1}{n^2})$
Here, $\Sigma_{n=1}^\infty \dfrac{1}{n}-\dfrac{1}{n^2} \geq \Sigma_{n=1}^\infty \dfrac{1}{n}-\dfrac{1}{2n}=\Sigma_{n=1}^\infty \dfrac{1}{2}$
we see that the series $\Sigma_{n=1}^\infty \dfrac{1}{2n}$ is a divergent harmonic series.
Hence, the given series Diverges by the direct comparison test.