Apply the Integral Test to determine the convergence of ∑n=2∞1nlnn\sum_{n=2}^{\infty} \frac{1}{n \ln n}∑n=2∞nlnn1.
The series converges because ∫2∞1xlnxdx\int_2^{\infty} \frac{1}{x \ln x} dx∫2∞xlnx1dx converges
The series diverges because ∫2∞1xlnxdx\int_2^{\infty} \frac{1}{x \ln x} dx∫2∞xlnx1dx diverges
The Integral Test is inconclusive for this series
The series converges because the terms approach 0