I I T 



P H- ^ = — 1 — t — 9 — iô — etc. =: — ^ 

 imdc elicitnr C = — -J^. 



§. 4. Quoties ergo fiieiit x -\- y z=l i , summa haruni 

 duarum seiierum junctim sumtamm: ^ -)_"''' -|---}-^^ -l- etc. 

 _j_^_f_^_i_^_l_-^_j_ etc. erit :i=: ^ — Ix .ly, hincque sta- 

 lim scquitur teitius casus supra memoratus. Sumto enim 

 X zz.},, erit quoque y:zzlf ideoqiie ambae hae séries inter 

 se acquales, iinde sequitiir fore 



r^= + r? + ,-^3 + s"-, -t- ^'<=- = ^r - 5 Ce)' = ^ -i (' ^Y- 



Praeterea vero, quoties fuerit a -\-hziz. 1 ponaturque 



a an . a'i , . ^ Ti b , b' , bi . . 



nr - -4- h etc. et B =. -\ \- etc. 



semper erit A + B ^: ^ — la . Ib. IJinc ergo si alterius 

 harum serierum sumina aliunde esset cognita, etiani alte- 

 rius summa innotesceret. llocque est illud ipsum proble- 

 ma, quod jam olim tractavi. 



P r oh 1 e m a II. 

 SI fuerit x — y nz 1 , hinas ill as formulas : pzrzf^ly et 

 qzzif ^Ix in scrics resolvere, ita ut hinc procleat 

 p -\- q izlIx . 1/ -[- C. 



S o 1 n t i o. 

 §. 5. Cum hic sit y m x — 1, erit 

 ly = l{x-i) =lx-^l (.-:) = lx----~-^-^, - etc. 

 hincquc ,;-/';/j=:J(/x}'-4-i+^-^+-',-t-j^;,+ etc. 



