Abstract

Based on the Newton-Cotes and Gaussian quadrature rules, we develop several new closed form approximations to the
mathematical constant e. For validating effectiveness of our approximations, a comparison of our results to the existing
approximations is also presented. Because of the level of mathematics, the presented work is easily embraceable in an
undergraduate class. Another aim of this work is to encourage students for formulating other better approximations by
using the suggested strategy.

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