Does ∑n=1∞nn3+1\sum_{n=1}^{\infty} \frac{n}{n^3+1}∑n=1∞n3+1n converge?
Yes, by comparison with ∑1n2\sum \frac{1}{n^2}∑n21.
No, by comparison with ∑1n\sum \frac{1}{n}∑n1.
Yes, by the Ratio Test.
No, by the Divergence Test.