# How do you show the sum of $1/(n\log n)$ diverges? [duplicate]

How do you show the sum $$\sum_{n=2}^\infty \frac{1}{n\log n}$$ diverges?

I have tried to use the ratio test but the outcome was inconclusive as the limit was equal to $1$.

• Integral test. Or, Cauchy Condensation test. – David Mitra Jan 29 '14 at 23:05