How do I show absolute convergence for the series
$$\sum_{n=0}^{\infty} \frac{n}{\sqrt{2n^5 +1}}$$
I have already showed by Comparison test that it is convergent. I am after the way of showing $\sum |a_n|$ is convergent. I tried ratio and root test but it gives me a limit of 1 so I need to do another test. I am so stuck in this part. Please help.
The terms of the series are positive, so if it converges, it converges absolutely. The comparison, ratio and root test are all for absolute convergence.