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!
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?
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real-analysis
sequences-and-series
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2Do you know the corresponding answer (more importantly, technique) for $\sum \frac{1}{n (\log n)^p}$? – 2011-08-07
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2Hint: Integral test – 2011-08-07
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0Hint: What’s the derivative with respect to $x$ of $\log(\log(x))$? – 2011-08-07
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2If you have the Cauchy condensation test, you can apply it twice and you'll have the answer. – 2011-08-07