152 DE QVANTITATIBVS 



(IH-.V)— ^_,,„1,^^ ^,- ^,^ ...(§. 17 ) 



ynde fimul ordo huiusmodi fbrmularum facile col- 

 gitur. 



Problema IV. 



24. Binomii potejlatem (i-f-.v)'* transformare in 

 huiusmodi progreffionem maxime conuergentem x 



denominatore exijlente niultlnomio quocunque. 



S o I u t i o. 



Si folutiones praecedentium problematum coti- 

 fulamus , Itui attentione adhibita inde fequentem fo- 

 lutionem generalem colligimus ; 



A = 



u . 



r^- 



,(p 



ico-(-Cp)(cD-^cp— I)* I. a 



r^ — colcu^ — Ofgj — t) (a->-(|));n-f-{t) — \)(ii-t-^—7) 



(cD-t-^.(to-|-$ — i)(oj-»-CI5 — 2/ 1. I. 3 



■rj co fgj — 0(to — ;'((») — ^) (Ti-t-(Il)(n+v|?-r)(>t +(p-?)(fl-|-$..ri 



(cjj-t-(P)(tjj-(-(p-iXtiJi-Cll-j;(aj^(J)_3/ " T. T. 3. 4 



etc. 



deinde vero pro denominatore : 



— (P :n — co) 

 "■ . (co -f- (p; 



g _ ( 1)[CD— ■ ) (rt — to ) (>!__ td -f^) 

 >. 2 (lO-f-$)($ _,_(p_,) 



Y — ^i^jniMrrj)^ (rt_— to) (n — co-f-i)(rt — co-»- ») 

 * 1- s. 3 * (co-t- (p)(co-f-(I)- i)(to-+-Cl) — s) 



*^ -- $($— ._ i)(Cl)— 5)((P_ 3) (r_co (n—co- t-. ) (r— to -i-,)(>i--co -f.?) 

 '. ». i. ♦ ' (co-f-(p),io-f-(f — 'Xt^-»-Cp — sjiio-t-^? — 3) 



etc. 



qui 



