Apply the integral test to ∑n=2∞1n(lnn)2\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^2}∑n=2∞n(lnn)21 and determine convergence.
The series diverges
The series converges
The integral test is inconclusive
The series sum equals π26\frac{\pi^2}{6}6π2