Is ∑n=1∞n2n2+1\sum_{n=1}^{\infty} \frac{n^2}{n^2+1}∑n=1∞n2+1n2 convergent?
Yes
No, the limit of the terms is 1.
Yes, by the Ratio Test.
No, by comparison with ∑1/n\sum 1/n∑1/n.