To test this series for convergence

$\displaystyle {\sum_{{{n}={1}}}^{\infty}}\frac{{{n}}}{\sqrt{{{n}^{{3}}+{6}}}}$

You could use the Limit Comparison Test, comparing it to the series $\displaystyle {\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}^{{p}}}$ where $\displaystyle {p}$=Preview Question 6 Part 1 of 2  

Completing the test, it shows the series: