## University Calculus: Early Transcendentals (3rd Edition)

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.