33G Aloysh Casinnlli 



q q^ _4 73 5.0^4 G.7.8 72 7.8.9.10 76 

 "^'^p^'~ 2 >~"*'2~3^~"2.3.4 V"*" 2.3 .4.5 J^ 

 72 4 73 5.G74 6.7.8 75 7.8.9.IO76 



— etc. 



^"'P'^ p p^'^Z'p'- 2.3yy7"*"2.3.4p9 2 . 3 . 4 . 5 /;""*"''^'^' 



qiiarum serierum lex per se manifesta est . 



Sigao non consideralo , harum serierum terminus genera- 

 lis est 



(w-f-l) (/w-i-2) (2m— 3) (2m— 2) y"' 



2.3 (in— .7.) (m— T) p'^m—\ 



cumque sit terminus subsequens 



(ro-H2) (7WH-3) (2m— 1 ) 2ot 7"-^' 



2.3 {nt—1)m p2m^i 



evidens est series esse convergentes si 



(w-)-2) (m-H3) . . . (2 m— 1)2m q'"-*-^ 

 2.3... (m— 1)m p2'"-^^ 



(m4-1) (;»H-2) . . . (2m— 3) 2 m— 2) 7" 

 2.3...(m— 2)(m— 1) p2m-i 



scilicet si 



seu 



et quoniam 



(4m— 2)-l-</w-»-l , 

 p^ 



„ 4m— 2 

 m-i-1 



4m — 2 



7M-+-1 



neqiiit esse major 4(7,secus enim esset Am — 2>4 7n-i-4 

 ergo erunt illae series convergentes si ;»2 > 4 ^ . 



Si autem erit p'^^Aq series illae erunt divergentes; atque 

 in hoc casu si coefficiens q est positivus , radices uti nolum 

 est erunt immaginariae ^ si vero q est negativus, tunc series 



reduci possimt convergentes hoc modo. Posito x=y± — , 



aequatio x'^:+:px — ^=0 trausformatur in 



