Does ∑n=1∞lnnn3\sum_{n=1}^{\infty} \frac{\ln n}{n^3}∑n=1∞n3lnn converge?
Yes, by comparison with ∑1n2\sum \frac{1}{n^2}∑n21
No, by comparison with ∑1n\sum \frac{1}{n}∑n1
Yes, by ratio test
No, because lnn\ln nlnn grows too fast