2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137362Translated from the Latin original, "Observationes generales circa series, quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur" (1777). E655 in the Enestrom index. Euler looks at the binomial expansion $(1+x)^n$ for $x=\cos ϕ+i\sinϕ$. He does $n=$ positive and negative integers, and $n={1/2}, -{1/2}$, and particular values of $ϕ$.12 pages. E655History and OverviewClassical Analysis and ODEs01A50text