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Infinite Serieseasy
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Consider ∑n=2∞1n(ln⁡n)2\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^2}∑n=2∞​n(lnn)21​. By the integral test, this series converges if ∫2∞1x(ln⁡x)2dx\int_2^{\infty} \frac{1}{x(\ln x)^2} dx∫2∞​x(lnx)21​dx converges. Which is true?