Introductio in analysin infinitorum

196 DE SERIEBUS LIB. I. Quæratur scilicet Seriei modo assumtæ summa ad terminum $P z^n$, atque ponatur $s=A+Bz+Cz^2+Dz^3+Ez^4+........+Pz^n$, quoniam hujus Seriei summa in infinitum constat, quæratur summa terminorum ultimum $Pz^n$ in infinitum sequentium, qui sint $t=Qz^{n+1}+Rz^{n+2}+Sz^{n+3}+Tz^{n+4}+\&c.$, hæc Series per $z^{n+1}$ divisa dat Seriem recurrentem propositæ æqualem, cujus propterea summa erit $t=$ $\frac{Q z^{n+1} + (R - \alpha Q) z^{n+2} + (S - \alpha R + \beta Q)z^{n+3} + (T - \alpha S + \beta R - \gamma Q) z^{n+4}}{1 - \alpha z + \beta z^2 - \gamma z^3 + \delta z^4}$. Unde orietur summa quæsita $s=$ $\frac{+ A + (B - \alpha A) z + (C - \alpha B + \beta A) z^2 + (D - \alpha C + \beta B - \gamma A) z^3 - [TRUNCATED]