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Infinite Serieshard
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For the series ∑n=2∞1n(ln⁡n)2,\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^2},∑n=2∞​n(lnn)21​, which inequality gives the best upper bound for the remainder RN=∑n=N+1∞1n(ln⁡n)2R_N = \sum_{n=N+1}^{\infty} \frac{1}{n(\ln n)^2}RN​=∑n=N+1∞​n(lnn)21​ by the Integral Test?