Is the series $\sum_\limits{n=1}^\infty\frac{n}{n^3+1}$ convergent or divergent?
Convergent series and divergent series $\sum\limits_{n=1}^\infty \frac{n}{n^3+1}$ and $\sum\limits_{n=1}^\infty \frac{n^2+1}{n^3+1}$