## Thomas' Calculus 13th Edition

Let us consider $a_n=(\dfrac{1}{n}-\dfrac{1}{n^2})$ Apply the direct comparison test. We can see that $\Sigma_{n=1}^\infty (\dfrac{1}{n}-\dfrac{1}{n^2}) \geq \Sigma_{n=1}^\infty (\dfrac{1}{n}-\dfrac{1}{2n})=\Sigma_{n=1}^\infty (\dfrac{1}{2n})$ Here, the series $\Sigma_{n=1}^\infty (\dfrac{1}{2n})$ shows a harmonic series which is divergent Thus, the series diverges by the direct comparison test.