Does the series ∑n=1∞2n2+3n2+1\sum_{n=1}^{\infty} \frac{2n^2 + 3}{n^2 + 1}∑n=1∞n2+12n2+3 converge?
Converges by the Limit Comparison Test
Diverges by the Divergence Test (Limit Test)
Converges absolutely by the Ratio Test
Converges conditionally by the Alternating Series Test