DiSQCISITIO ANALITICA ETC. l55 



C=_24. -^„ =_2i ^^'"'''''"^ 



5040 ~ ■ 2.3.4.5.G.7 



4 

 6769 (1,2,3,4,5,6,7) 



" — 40320 —■''*■ 2.3.4.5.6.7.3 



5 



67234 (1,2,3,4,5,6,7,8) 



IT 9a — 9i > - 



^ — "~'' 362880 — — ^^- 2.3.4.5.6.7.8.9 



etc. etc. etc. 



Hiuc 



1 2 3 



. S.4 (1,2,3,4) (1,2,3,4,5) , „ (1,2,3,4,5,6) 



( log. (1+.) ) =.._24L^.=4-2lVm^-^-24-^23X5Z7 ^'-^ ^"=- 



cujus scnei terminus generalis est 

 ±24 



(1 2 3 4 " . . (n-H2) ) n^3 



2.3.4 . . . (n-^i) 



sumpto signo -h si ra est numerus impar, signo — si n est 

 numcrus par. Cum ergo sit 



1 2 3 



/■ \i 0.2) (1,2,3) „ (1,2,3,4) 



( log. (1+x) y = .r^_ 2 ^ « ^+ 2 ^^ .. - 2 'j^ xs+ 



etc. 



n-1 



(1,2,3 ...„) 



n-4-1 



2.3.4.5 . . («4-1) 

 (log. (1+x); =x3-6 -23J x'-H6_ — -- x^- 6 yUU ''+*"=• 



,(1,2,3 ".\(„+1)) 



I ^_^__ — x" ■+■- 



2.3.4 . . . (n-t-2) 



2 3 



/. M. ^^* . ^/Ij^illi^ 5_._9.^!:2M!) 6 „ . (1,2,3,4,5,6) ^, 

 ( log. (1+x) ) =x«- 24-23^x^+24^3-^3^x6-24 ^-_^x'+ 



etc. 



(1,2,3. °.(n+2)) 

 2.3.4 . . . (n+3) 



