Use the Direct Comparison Test to determine the convergence of ∑n=1∞1n2+n\sum_{n=1}^{\infty} \frac{1}{n^2 + n}∑n=1∞n2+n1
Converges, since 1n2+n<1n2\frac{1}{n^2 + n} < \frac{1}{n^2}n2+n1<n21 and ∑1n2\sum \frac{1}{n^2}∑n21 converges
Diverges, since 1n2+n>1n\frac{1}{n^2 + n} > \frac{1}{n}n2+n1>n1 and ∑1n\sum \frac{1}{n}∑n1 diverges
Converges, since 1n2+n≈1n\frac{1}{n^2 + n} \approx \frac{1}{n}n2+n1≈n1 for large nnn
Cannot be determined with the Direct Comparison Test