S^ DE SERIERVM 



Problenia V. 



§. 36". Itiaenire termi.mm gencralem (ericrum recur- 

 rentium lcainJi ordinis » in qjibji quilibet termin is ac« 

 quitur a^^regito binorum termimrum anceccdentiam per 

 quoicunqje numeros mukiplicacorum : 



Solutio. 



Sit terminus indici x refpondens ~y\ 

 terminiis indiciA:-i rcfpondens zi: y 

 terminus indici.r-2 rcfpondens — ^y 

 haecque propofiti fit lex fcrici recurreatis , vt fit : 



Quia igitur eft 



J' — j~ 'dx~T- ,, _ix* rj.jU» ~T~,.-. ..ii* *" etc. 



J — J' idx~i" i-iic» ~ i.-.*ijc»~i~ '..i.^JU* ' CtC» 



erit Iiis fc)rmulis fubflitutis : 



, / 6y . diy d*y , d*y » 



^"^ J ,./xH-,.jx« - ,.-.,ix» -*- .^ITx.* - ctc; 

 Ad quam acquationcm rclbkicndnm ponatur (ccundum prae- 

 ccptum gencrale i pro^ \ 2 pro ^ \ z* pro ^^ ctc. fictquc 



_i_Vi_ *-!---, - - - _f_ ■ ctc. ) 



— 1-6( I - — _U - - _l CtC. 1 



quae aecjuatio ad hanc formam finitam redncitur , 

 I — a'-'" *-|-S^~'* : cuins faclorcs inucdigarc oportct. 

 Pofito crgo f"+"* —u ac ref^)lnatiir hacc acc]natio uu — 

 fta_4_g; cuius vel ambac radices funt realcs , vcl anibac 

 imagin.iriac , vcl dcniqiic ambac inicr fc aequaics. Ho&- 

 quc troi cafus (corfim cuoluc oportct. 



I. Sint 



