166 m TERMimS GENEKALIBVS 



qiiiciinqiie conflans practcr vnitatcm qiio cafii fatis- 

 facit terminus generalis nx—fi-\-i. Si datae feriei 

 duo priores termini fint a. et (3. lex progreflionis 



2 



™J_— C. erit terminus gcneralis huius feriei 



[xx—3x-h-2}2x-l 



Vh L- 6(.c. 



x-2 



Q. 



Quod ad alterum gcniis progreiTionum attinet 

 in quarum formulis quantitas variabilis .v rcperitur, 

 fatendum quidem eft dariferics progrelTionis planae 

 ac pcrfpicuac, vt A.i— B; A-H^ii^B&c. quarum ter- 

 mini generalcs adliuc defiderantur , fed tamcn e 

 contrario multac quarum progreflio perquam ob- 

 fcura eft ad terminum generalem adhibita induftria 

 reduci poffunt •, fic data lege progreflionis A.v-f- 

 (;v'-|-i)'^— .v(.v— i)'^"^'"^ non illico apparet formu- 

 lam terminorum qui huic lcgi refpondcant effe 

 ,v"^ -1- (.V— i)'"'^' vel formulam term>inorum qui re- 

 fpondeant legi ?n{k-a'^)-\-a'^~^^ ~B effe a^^-^-m^. vel 

 legcm progrelfionis A.v-f-(.v-l-i)*-^-' — .v(x-i)''— B. 

 conuenire termino generali .v*-f-(vV- 1 ^^^. fi ncmpe 

 in his exemplis fumatur x pro exponente termini 



dati A. 



V. Sed quaecunque fit ifta progrcflionum va- 

 rietas , certim eft feries omnes ad terminum gene- 

 rahim faltem infinitum reuocari pofle. Sit enim 

 data feries 



(A)/7-}-b4-r^-^-+-&c. 

 erit formula eius feu terminus gencralis niltem in- 

 finitus 



