i5o Aloysii Casinelli 



Comparaiione hujus seriei cum praecedenli deducenius 



m 

 mA=: (m-|-1) A' | < - 



(m4-1 ) m 



mB=(m4-2)BH 2~A- T 



(m4-2) (m+l ) TO 



(,«J-3) (m-4-2) (m+1) TO 



IT-. ■ rxT. , ("'+^) ^ (m+3) ^ _ (m+2)„ (m+1) to 



etc. etc. etc 



Sen 



TO 



(m-f-1) TO 



■xr ("'+2) (m+1 TO 



3C=:--2-B+— ^jA-- 



dn ('"+3) (m+2) (TO+1) ,„ 

 4D = --2-C+-^B ^A+20 



. r ("'+^) r. , ("'+3) (m+2) (m+1) TO 



etc. etc. etc. 



Qua lege progrediantur hae formulae per se manifestum est, 

 atque si dicantur M,L,K, H etc. coefficientcs terminorum se- 

 riei («-t-i) csimi, n esimi , (n — i) esimi , (« — 2) esimi 

 etc. erit 



'»M = 2 "^ 6 12 "^ ^"^' 



(to + 3) (to +2) (m+1) TO 



~" -Cd: „ ■' Brp , ./ a±:- 



■^(n — 3) (,j_2) (» — 2) (/J — 1) "^(n — 1)n — D(„4-1) • 



sumpto signo superiore si n-Hi est numerus impar, in- 

 fer! ore si «H-i est numerus par. Verum hie coefficiens M, i- 



