Identify which series converges by the basic comparison to ∑1n2\sum \frac{1}{n^2}∑n21.
∑n=1∞1n2+n\sum_{n=1}^{\infty} \frac{1}{n^2+n}∑n=1∞n2+n1
∑n=1∞1n\sum_{n=1}^{\infty} \frac{1}{n}∑n=1∞n1
∑n=1∞nn2+1\sum_{n=1}^{\infty} \frac{n}{n^2+1}∑n=1∞n2+1n
∑n=1∞n2n2+1\sum_{n=1}^{\infty} \frac{n^2}{n^2+1}∑n=1∞n2+1n2