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I'm having some trouble approaching this problem. "For what values of $p\in\mathbb{R}$ does the series $$\sum^{\infty}_{n=4}{\frac{1}{n\log (n)\log( \log(n))^p}}$$ converge?" For a fixed p, I could see approaching this with some of the standard tests for convergence but I am unsure how to find p. Any answers or hints would be appreciated, thanks!

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    Do you know the corresponding answer (more importantly, technique) for $\sum \frac{1}{n (\log n)^p}$?2011-08-07
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    Hint: Integral test2011-08-07
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    Hint: What’s the derivative with respect to $x$ of $\log(\log(x))$?2011-08-07
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    If you have the Cauchy condensation test, you can apply it twice and you'll have the answer.2011-08-07

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