De seriebus divergentibus

TL;DR

Euler explores the use of divergent series in calculus, providing arguments, definitions, and evaluating a specific divergent series to approximate its sum, contributing to the foundational understanding of divergent series.

Contribution

This paper introduces Euler's own definition of the sum of a divergent series and evaluates a specific divergent series to approximate its sum.

Findings

Euler's definition of divergent series sum

Approximate sum of the series 1 - 1 + 2 - 6 + 24 - 120 + ... is 0.5963473621372

Arguments for and against divergent series in calculus

Abstract

Euler gives a long introduction, giving all the arguments for and against the use of divergent series in calculus and then gives his own definition of the sum of a diverging series. Then in the second half of this paper he evaluates the the 1-1+2-6+24-120+720-... on several ways and gets the sum 0.5963473621372. The paper is translated from Euler's Latin original into German.