7« DE SERIERVM 



Vnicus cafiis hic excipitur quo m~i y ob denominato- 

 rsm m—i eiwnefcentcm. Cum enim hoc cafu habcatur ; 



^4-A.r=:^,-i-7^.H-T4:fo H- etc. 

 ad terminum bx tolleudum huiubmodi \alor pro y accipi 

 ^Q}x.tyz:zk-\-V>x-^Cxx-\-v: \nde fit ^^ — B-+2C* 



-|-'"et ^4|-2C^-li^' : ficquc habcbitur : 



C 



Fiat ergo C — \b^ et B— a — ;^; critque vzrP , ct ter- 

 ipinus gcneralis y — X-\-[a-\b)x-\-\bxx-\-V\ (eu 

 cum A in fundione P compreliendi poflit , cht -.y::^ (<^~i^) 

 x-\-\bxx-\-?. Q. K. I. 



Scholion. 



§. 54. Huiusmodi nutem (eries rcnocari polTunt ad 



legem recurrcntium fimplicium. Cum enim fit 



y' — a -\- b X -\- my crit 



y^' — a-\-b {x-\- 1 )-f- my' \nde fubtrahcndo 

 y" -y'— b-\-my^ -my fimili modo erit 



j, ///_^,//— /^ _|_ jjjy//_f„y/ dcnuoquc fubtrahcndo : 



y^ -iy'^-\-y'—my''' -^my'-\-i?iy (lu 



j'''^n:(w-l-2]>'^''-(2w-hi)>'^-t7;i;' fine pro tcrminis antcccdcntibns 



y —'m-^-i/y-^im-^-iyy-^-m^^y. 



Hinc crgo fccnndum §. LI. formabitur acquatio : 



u—(m-\-2.)u*-\-{2in-\-i)u—m—o quae habct fiiflores : 

 («—I )'(«—»/)— o, cx quibus oritur terminus gcncralis : 

 y~V-\-Qx-\-JifR. lam vt hacc forma nimis late patens 

 ad cafum propofitum j'—<j-f ^A* +;//>' accommodctur , ob 



y- 



