Show that ∑n=2∞lnnn\sum_{n=2}^{\infty} \frac{\ln n}{n}∑n=2∞nlnn diverges. Which test is most direct?
Integral Test: ∫2∞lnxxdx=∞\int_2^{\infty} \frac{\ln x}{x} dx = \infty∫2∞xlnxdx=∞
Direct Comparison with ∑1n\sum \frac{1}{n}∑n1 (diverges)
Limit Comparison with ∑1n\sum \frac{1}{n}∑n1: limit = ∞\infty∞ → diverges
All of the above work