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The Flint Hills series, is the series $$\sum_{n=1}^\infty\frac{1}{n^3\sin^2(n)},$$ and it's an open problem as to whether the series converges. From Corollary 3 and the proof of Corollary 4 of this paper, it seems that it's also unknown if $$\lim_{n\to\infty}\frac{1}{n^3\sin^2(n)}$$ converges. Ge...