Use the limit comparison test with ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}∑n=1∞n21 to determine convergence of ∑n=1∞2n+1n3−1\sum_{n=1}^{\infty} \frac{2n+1}{n^3-1}∑n=1∞n3−12n+1.
Converges
Diverges
Converges absolutely only
Cannot be determined