%0 Journal Article %T De seriebus divergentibus %A Leonhard Euler %A Artur Diener %A Alexander Aycock %J Mathematics %D 2012 %I arXiv %X 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. %U http://arxiv.org/abs/1202.1506v1