The error in an alternating series
Mark B. Villarino
TL;DR
This paper presents new proofs for refined error estimates of alternating series and the Euler transform, enhancing understanding of their convergence and accuracy.
Contribution
It introduces novel proofs for Johnsonbaugh's refined error bounds and the convergence of the Euler transform, based on ideas from R. M. Young.
Findings
New proof of Johnsonbaugh's refined error estimates
New proof of Euler transform error estimate and convergence
Enhanced theoretical understanding of alternating series
Abstract
We give a new proof of Johnsonbaugh's refined error estimates of an alternating series based on an idea of R. M. Young. We also give a new proof of the error estimate and convergence of the Euler transform.
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