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∑n=2∞1(lnn)ln(lnn) \large \sum_{n=2}^\infty \dfrac1{ ( \ln n)^{\ln (\ln n) } } n=2∑∞(lnn)ln(lnn)1
Does the series above converge or diverge?
Hint: For x≥2x\geq 2x≥2, ln(x)<x\ln(x) < \sqrt xln(x)<x.
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