Ononot — The Cauchy Condensation Test states that for a positive decr

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Infinite Serieshard

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

Apply this test to determine the convergence of $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{3/2}}$ .

Which statement is correct?