1. {66) ■ 



fumma erit zz: — 5 — ciiius fnidionis euolutio manifefto rro- 

 ducit iflam fericm. Plura exempla adiungere fuperfluum fo- 

 rctj qui.i hoc argumentum iam alias fufuis cll: traclatum. 



Problema III. 



Sl ^'t ante X denotct funclionem qnamcunque tpjius x , quae 

 Joco X fcrlbendo fucccjjiue x -f- 1 , x 4- 2 , x -f- 3 , abcat jn X', 

 X\ X'^\ ac proponaiiir fcqiicns ferles infinlta cum pragrcjfone 

 hjper^eometrica commifla : 

 - — - I. 2. 3. 4.. ... X. X 



g; — I. 2. 3. 4. . . . (x-l-i)X'' 



H- I. 2. 3. 4. . . . {^-\-ci)X'^ 



— etc. 

 eius fummam inuejligare. 



ui.;.;i-i Sokitio. 



§. 55. Statuatur ifi:a fumma quaefita ~ i. 2. 3. . . ^"5, 

 ita vt tantum fundionem S indagari oportcat, eritque 



S = X— (jkT-H I )X^-^(A--t- 1 ) (.VH- 2)X^' — {X-+- 1 ) (.v^ 2) (.v-^3 )X^''''-(- ctc. 



Hinc ergo 11 loco x Ybiquc fcribamus x -t- i, fiet 



S' — X'—-{x-^ 2) X'' -j- (v -+- 2) (.V -^ 3) X''' 



— (x -+- 2) (.V -f- 3) (a- -^ 4) X^^^^ -+- etc. 



quae poflerior feries per .v -f- i multiplicata ac priori adieda 

 producet i(bm acquationem: S -1- (-v -j- i) S'' — X, cx qua 

 ergo valorem ipfuis S definire oportct. 



§. 3<J. Hic autem pro S talcm feriem per diffcren- 

 ti.ilia ipfuis X procedentcm fingerc non licct vt fupra, prop- 

 tcrca quod fundio 



pcr fadorcm variabilem .v -}- i efl: multiplicata, quamobrcm 

 pro S affumamus feriem generalcm p -i- q -'r y -^- s -i- ( -+- etc. 



quae 



