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Infinite Serieshard
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The Cauchy Condensation Test states that for a positive decreasing sequence {an}\{a_n\}{an​}, the series ∑an\sum a_n∑an​ converges if and only if ∑2ka2k\sum 2^k a_{2^k}∑2ka2k​ converges.

Apply this test to determine the convergence of ∑n=2∞1n(ln⁡n)3/2\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{3/2}}∑n=2∞​n(lnn)3/21​.

Which statement is correct?