On divergent Series

TL;DR

This paper presents Euler's exploration of divergent series, focusing on the example 1! - 2! + 3! - ..., and discusses methods to assign a sum to such series, estimating it around 0.59.

Contribution

It provides an English translation of Euler's original work on divergent series and details his methods for summing specific divergent series.

Findings

Euler's methods for summing divergent series

Approximate sum of 1!-2!+3!-... is 0.59

Insights into early understanding of divergent series

Abstract

This is the translation of Leonhard Euler's paper "De Seriebus divergentibus" written in Latin into English. Leonhard Euler defines and discusses divergent series. He is especially interested in the example $1!-2!+3!-\text{etc.}$ and uses different methods to sum it. He finds a value of about $0.59...$.