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I know that $$\sum_{n=3}^{\infty}\frac{1}{(\log n)^{\log n}}$$ converges and hence applying the Comparison test, I get the ratio $$\frac{a_n}{b_n}=\frac{(\log n)^{\log n}}{(\log n)^{\log\log n}}.$$ What I want to know is whether $a_n/b_n$ is bounded above or not. Or is there different approach to solving this problem?

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  • $\begingroup$ Cauchy's condensation test readily gives the answer. $\endgroup$ May 22 '17 at 15:55
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I should have searched before. The answer was here. Sorry for redundancy.

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