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arXiv · 2007.11017

Convergence of a sinusoidal infinite series from Borwein, Bailey, and Girgensohn

Ravi B. Boppana
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Abstract

Borwein, Bailey, and Girgensohn (2004) asked whether the following infinite series converges: the sum of $(\frac{2}{3} + \frac{1}{3} \sin n)^n / n$ over all positive integers $n$. We prove that their series converges. The proof uses the irrationality measure of $\pi$.

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Ravi B. Boppana. 2020-07-21. Convergence of a sinusoidal infinite series from Borwein, Bailey, and Girgensohn. https://arxiv.org/abs/2007.11017

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