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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 $1$.

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    $\begingroup$ Integral test. Or, Cauchy Condensation test. $\endgroup$ – David Mitra Jan 29 '14 at 23:05

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