so if I use the comparison test to determine whether the infinite series, $\displaystyle \sum\limits_{n=1}^{\infty}\frac{1}{\sqrt{2n^3 + 7n}}$, and using $\displaystyle \frac{1}{n^{\frac{3}{2}}}$ as the comparing series....should the initial infinite series be convergent or divergent

my belief is that it should be divergent because $\displaystyle \frac{1}{n^{\frac{3}{2}}}$ is divergent and it is greater than $\displaystyle \sum\limits_{n=1}^{\infty}\frac{1}{\sqrt{2n^3 + 7n}}$

Thanks in advance for any help provided