i56 Aloysii Casinelli 



inductione facilime deducemus 



1 2 3 



/ N, (1,2,3,4,5) (1,2,3,4,5,6) ,„^ (1,2,3,4,5,6,7; 



n-1 



(1,2,3 . . . (n4-3)) 

 -^^'^ 2.3.4... (;;4-4) "- 



quae series simpliciores reddi possum scilicet 



1 2 3 



( N (1,2) (1,2,3) , (1,2,3,4) 



(1,2,3°. ! . ») 

 3.4.5 . . . (n+1) 



.rn-f-l 



/, .1, N>3 . 0'2''3) (1 ,2,V4) (1,2,3,4,5) 



(log. (H-x)/=x3 J- x^Jr 45 ^^- 4.5.6 x«+ eic. 



(1,2,3°. .(«-Hl) 



j;in-. 



■> 



~~ 4.5.6 . . . («+2) 



/. M, ^M . (Will 5, (WA^ . (1,^>3,4,5,6) 

 (log.(1+x)y=x« 5—-'+ 5.6 "'- 5.6.7 " "^ 



etc 



(1,2,3.°..(n+2) 

 5.6.7 . . . (n+j) 



/I M_L_ AX5 5 (1,2,V4.5) ^ , (1,2,3A5 ,6) ^ (1,2,3,4 ,5,6,7) 



(1,2,3° . ■ (n+3) 

 6,7,8 . . . {n-\.\) 



xn-i-4 



etc. etc. etc. 



E.t his autem seriebus generalim deduceraus 



1 2 



/'wM-l_^^™ n, 0A3...m) „^i . (1,2,3..( m4-1)),m^2 (liM^ll(':±HlL ,B,^3_, 

 (^log.(l4.x); =:xn. -^-^, ^__^__x _____^^^^ 



n-1 



(1,2,3 . . . ('m-4-«_2)) 



-(- jm-t-n— T 



(^4-1 )(m4-2). . .(m-t-i— 1 ) 



