Determine whether the series $\sum_{n =1}^{\infty} \frac{n + \sqrt{n}}{2n^3 -1}$ converges?

Determine whether the series $ \sum_{n =1}^{\infty} \frac{n + \sqrt{n}}{2n^3 -1}$ converges?

My answer: For large n, the given series is smaller than $ \sum_{n =1}^{\infty}\frac {2n}{2n^3}$ which is equal to $ \sum_{n =1}^{\infty}\frac {1}{n^2}$ , but we know that the later is convergent by the p-series test, then by comparison test the given series is convergent.

Is my answer correct?