Meditations about a singular type of series
An Italian translation of this work has been done by Carmine Suriano.
Euler examines the series sm,n = 1 + 1/2m∙(1+1/2n) + 1/3m∙(1+1/2n+1/3n) + 1/4m∙(1+1/2n+1/3n+1/4n) + .... He gets a relation 2sn,n = sn2 + s2n, along with some similar, more complicated formulas. Then he evaluates sm,n for m+n = 6.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 20, pp. 140-186.
Opera Omnia Citation
Series 1, Volume 15, pp.217-267.