Use the Limit Comparison Test on ∑n=1∞n+5nn5/2+n2\sum_{n=1}^{\infty} \frac{\sqrt{n} + 5n}{n^{5/2} + n^2}∑n=1∞n5/2+n2n+5n. Which series should you compare to?
∑1n\sum \frac{1}{n}∑n1
∑1n3/2\sum \frac{1}{n^{3/2}}∑n3/21
∑1n2\sum \frac{1}{n^2}∑n21
∑1n\sum \frac{1}{\sqrt{n}}∑n1