Answer by Bernard for Prove that $\sum_{n=1}^{\infty}\log \cos \left...
As $\;0<\cos\frac 1n<1$, we have $\;\Bigl|\log\cos\frac1n\biggr|=\log\biggl(\frac 1{\cos\tfrac1n}\biggr)$. Now $\cos\frac1n=1-\frac1{2n^2}+o\bigl(\frac1{n^2}\bigr)$, so$$\frac...
View ArticleProve that $\sum_{n=1}^{\infty}\log \cos \left (\frac{1}{n}\right )$...
Prove that $$\sum_{n=1}^{\infty}\log \cos \left (\frac{1}{n}\right )$$ converges absolutely.The answer here suggests to use the Limit Comparison Test but it works for $a_n \geq 0$ while $\ln(\cos...
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