2022
DOI: 10.1007/978-3-031-21460-8_3
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Monotonicity of Certain Left and Right Riemann Sums

Abstract: In an otherwise instructive 2012 article, Szilárd András provided a flawed argument purportedly establishing that the left (resp. right) Riemann sum of f (x) = 1 1+x 2 with respect to the uniform partition of [0, 1] into n equal intervals is monotonically decreasing (resp. increasing) relative to n. A few years later, D. Borwein, J. M. Borwein and B. Sims developed a symmetrization technique that allowed them to provide a rectified proof that the right Riemann sum of f (x) = 1 1+x 2 really is monotonically inc… Show more

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Cited by 3 publications
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