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Does the series: $$\sum\limits_{n=2}^{\infty} \frac{\cos(\log{n})}{n \cdot \log{n}}$$ converge or diverge?

I know that $|\cos(\log{n})| \leq 1$, but I really cannot apply it here. Any ideas on how to attack this problem

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    A quick try using $|\cos(\log{n})| \leq 1$ and the integral test gives that the $n$th partial sum is $\leq log(log(n))$, so if this diverges it does so very slowly.2011-03-23
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    On the other hand, the positive and negative terms "should" cancel each other out for the most part. I expect convergence.2011-03-23
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    I expect it to converge... Probably try a variation of generalized alternate test (Dirichlet test)?2011-03-23

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This problem appears in the Nordic university-level mathematics team-competition, NMC, 2010, with solution at the beginning of the following pdf: http://cc.oulu.fi/~phasto/competition/2010/solutions2010.pdf.

The search was series "cos(log(n))".

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    And just for the record: the answer is that the series converges.2011-03-23
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In case the link Jonas gave would be broken in the future, here is the solution:

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