An Interesting Analysis on a Curious Convergence Series

Abstract

The authors extend the work of Kempner as they investigate a peculiar convergence series derived from the harmonic series through the exclusion of terms containing specific digits in their decimal representation. The authors introduce a novel set S and its corresponding series S' which converge under certain digit-exclusion criteria. By generalizing this approach, they explore the mathematical and pedagogical implications of such series, highlighting their potential to enrich student experiences with proof and inspire further research in series convergence. This work not only broadens the understanding of Kempner’s series but also invites educators and mathematicians to reconsider the convergence of series through the lens of digit exclusion.