Apply the limit comparison test with ∑1n\sum \frac{1}{n}∑n1 to determine convergence of ∑n=1∞2nn2+5\sum_{n=1}^{\infty} \frac{2n}{n^2+5}∑n=1∞n2+52n.
Converges because the limit ratio is positive and finite
Diverges because the limit ratio is positive and finite
Converges by direct comparison
Cannot be tested