# Cannot figure out what test to use for this series.

I have this series and I am trying to determine if it is convergent or divergent. I already tried the comparison test and it seems to fail but only perhaps because I am breaking apart the sequence incorrectly.

$$\sum_2^\infty \frac{n+30}{n^2\sqrt n}.$$

• limit comparison test? – user99914 Nov 23 '15 at 5:17
• use the universal convergence test – Thoth Nov 23 '15 at 5:19
• You can divide top and bottom by $n$, then use direct comparison. – James Nov 23 '15 at 5:21
• I triedthe limit comparison test but perhaps by setting b(subn) as $\frac{n}{n^{2}\sqrt{n}}$ is not correct? – Erik Nov 23 '15 at 5:21
• For limit comparison your $b_n$ is fine. Maybe more simply observe that the top is $\le 31n$. – André Nicolas Nov 23 '15 at 5:27