SERIES SFMMANDI VLTERIVS FROMOTA.i^x 

 rummanda erit ob /X dxzz — l,^ ^ — ^^ , j^j — "~J; ~ 



etc <s — -!- -1- -L- _u -^ ^^_s.lL^ fc^ _i_ sh»_ 



CtL. O — 6x ~r- j^J -7-6a:«~ 3ox» "+- ^j^' "soa:» ~r ^s;^'» 



fig.fc" , 76" 36I7&'» , 24JT:;7pf ^ - 



-,7T^l^-i-^»-7;^r>-f-7:;7^'"*"-etc. qiuie expref- 

 fio conrtantcm non rtquirit, cum per fe euanefcat po- 

 fito x~co. Eo magis luitcm conuergit haec feries , 

 <5uo maior fuerit .v refpedu ipfuis b. Qiiare fi datae 

 feriei aliquot tcrmini initiales addantur aiftu , reliquorum 

 hnc mcthodo fumma inuenta lUi aggregato addita dabit 

 fummam propofitne feriei in infinitum continuatae, 



§. 8. Sed miflis his, quae priorem regulam tati- 

 tum commodiorem reddunt, progredior ad feries fum- 

 fnandas, ad quas illa formula non fufficit. Sit nimi- 

 fum feries fummanda, in qua figna terminorum alter- 

 nantur, vti 



a, a-^-b, a-H:6, a-+-i&, x, x.+-b 



A-B-^C-D -|-X-Y = S 



in qua ferie cum fit Y talis fundio ipfius x-{-l> quah's 

 X eft ipfu^s .V, erit Yz^X -f-?L^H-f^^-|-^£- 

 H- etc. Dcinde fi in S loco x ponatur .v— 2^ pro- 

 dibit S-X -f- Y ; erit ergo - Y -+- X =: '^^ - ^^.-f- 



^^ tb^dlJ, __t6b*d*s ■ zib* d> S _ p* ^'^'^ 6^a»X 



"T-i.^sdx' I 2.J. ♦.dx*'*i"t.2.j. + .sdx' "^- ~iTdx—7TdS* 



6»d»X b*d*X ^_ T)..,.,^,.. ds adX , td^X 



- rrrrdxr - -,T7r^^* - etc. Ponatur ^ = ^ -i- -^^-r- 

 ^^^^ -H ^"5^ etc. et comparandis terminis homologis 



X 'bdX b^ddX ib^^d^X b*d*X gbSdiX 



prodibit S — C-5-:^^- ,d;,a — yedx^ 



- etc. et introduccndo Y erit S — C ~hY ~hf-\-~Sy, 



^^T^fr^-^rrTi:^^» etc. Atquc ideo eritA-B 



-f-C 



