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Infinite Serieshard
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Use the Integral Test to determine the convergence of ∑n=2∞1n(ln⁡n)0.99\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{0.99}}∑n=2∞​n(lnn)0.991​. Evaluate ∫2∞dxx(ln⁡x)0.99\int_2^{\infty} \frac{dx}{x(\ln x)^{0.99}}∫2∞​x(lnx)0.99dx​ and determine convergence.