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
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
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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