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

2020/07/21 by Boppana, Ravi B.
#40A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2007.11017

Abstract

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

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