41 



T h c r e m a spéciale. 

 §. 33. Si hahcantur hac séries sibi affines: 

 A =z — H ^ H —, + etc. et 



1.3 ' 9 .33 ' 2Î ■ 3' ' 



.B = 7^ -+- 7^ + ;:^3i H- etc.; tum erit 

 2A H- B = ^ — î(Z3^ 



Demonstratio: 

 Cum ex theoremate primo, sumto x'=r^=:î, sit 



7^ H ^ + ^-^ -f- etc. =1 ^ — î (/ 2)% haec séries sequenti 



modo resoluta repraesentari potest : 



2(— -+--h-^--5-^etc.)— i(-î ^ + -^-etc.)r:^--ï(^2K 



V1.2 9.2J 25. 2J ' Vi.2 4-2^ 9. ai / lï 2 V / 



Nunc vero per theorema IV., sumto x m ï et /:::!: ï, ha- 



bemus hanc aequationem : 



-^ + -V3 + ,-7^5 ^- etc. = ^ - ? Z 2 . Z 3 _ ^ _ JL, L^ _ etc. . 



1.2 9.2-) 25. 2> S - 1.3 9-3^ 2J.3S 



Deinde vero ex theoremate secundo ^ sumto x =1 2 et 

 yzizZ, erit : 



-^ ^-f--^— ^-+- etc. — ï (/2)2 -^ -!- 4- -L^ -f— ^ + etc. 



1,2 4.1^ 9.2Î i6.24 i; ^^2/ 1.3 4.3- 9.33 »->->^» 



Substituantur jam hi valores loco illarum serierum, ac pro 

 parte sinistra prodibit : 

 :lzI_Z2 ./3-2(-^+-^-^--^4-etc.)1 



4 ^i-i 933 25-3Î Ji Tir l/IoV 



~M^!)' — (r^^--+--3 -netc.)) ""'^ ^^ ^* 

 Unde concludimus fore : 



2(^H--4-+-_L.--^etc.)1 

 -^ 1 (-i- ^ _i_ ^_ _J_ _^ etc.)J - ^ - • ^-^ ^ ^ -"^ ^^^'*''' 



= ^"-ï(Z3)^(ob (/i)^ — (Z3)^-2Z2 .Z3 4-(Z2)^). 



iM/wo/Vf; <f< f ^<:;a</. T. ///. . ^ 



