# How do you use the direct Comparison test on the infinite series sum_(n=2)^oon^3/(n^4-1) ?

Since ${n}^{3} / \left\{{n}^{4} - 1\right\} \ge q {n}^{3} / {n}^{4} = \frac{1}{n}$ for all $n \ge q 2$ and ${\sum}_{n = 2}^{\infty} \frac{1}{n}$ is a harmonic series, which is known to be divergent, we may conclude that ${\sum}_{n = 2}^{\infty} {n}^{3} / \left\{{n}^{4} - 1\right\}$ also diverges by Direct Comparison Test.