I have this series given by $$\sum\limits_{n=1}^\infty \frac{1}{n^3 \sin^2n}.$$ I know that the terms are all nonnegative. Can I get a subsequence of $\frac{1}{n^3 \sin^2n}$ such that its sum diverges to $+\infty$?
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11Flint Hills series? The question is open, depending on irrationality measure of $\pi$ – Alexey Burdin May 17 '15 at 20:51
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2See also http://mathoverflow.net/questions/24579/convergence-of-sumn3-sin2n-1 – mrf May 17 '15 at 20:58
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Alright. I see! – OKPALA MMADUABUCHI May 18 '15 at 16:49