Determine the convergence of the series 1/(n ln n) using the integral test.

Vault Of Euclid

Divergence of the Series 1/(n ln n)

Sequences core

Determine whether \( \sum_{n=2}^{\infty} \frac{1}{n \ln n} \) converges.

The solution and a full step-by-step explanation are here. Sign in to read them.

Tests the ability to apply the integral test, verify its conditions, and evaluate an improper integral using substitution.

This is a classic example in Calculus II courses when introducing the Integral Test, demonstrating a series that diverges very slowly.