Determine the convergence or divergence of the series ∑ (n=1 to ∞) n / (n^3 + 1).
Correct: A
Using the Limit Comparison Test with ∑ 1/n^2 (which converges by the p-test with p=2 > 1): lim (n→∞) (n / (n^3 + 1)) / (1/n^2) = lim (n→∞) n^3 / (n^3 + 1) = 1. Since the limit is a finite positive number and ∑ 1/n^2 converges, ∑ n / (n^3 + 1) also converges.