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# Series converge or diverge?

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Hi can I get some help on this

The problem statement, all variables and given/known data

Determine whether the series converges or diverges.

$\sum \frac{lnk}{k^3}$

The attempt at a solution

Since lnk always less than 0, so $\frac{lnk}{k^3} \leq \frac{1}{k^3}$ and $\frac{1}{k^3}$diverges so$\frac{lnk}{k^3}$ diverges.

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The divergence test is done by taking the limit of the main term. In your case, you have to take the limit of [ ln K / K^3.] To do that , you have to apply L'Hospital's rule, and differentiate numerator and denominator. In that case, you will get the limit of [1/3K^3]. If that limit is 0, then the series is converging. If not, then it diverges.

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• 1 month later...

The criterion above is not sufficient, for your case it is ok, but for example the series :$\sum_k\frac{1}{k}$ diverges even if the term tends towards 0.

You have comparison criterion or integrating instead of summing, but i do not have here the condition of applicability.

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