78 DE SVMMATIONIBVS SERIERVM 



§. 7. Vtidcciinquc principiiim noftrum con- 

 tcmplcmur , mirificum manifclbt conrenfum. Ad- 

 dantur fcries (A) cuiui fummam inuenimus — i et 

 feries (B) — ? , oportet vt (iimma ab additione oria- 

 tur ~ ff. Nempe oritur : 



(A) I — i_-i-i— i-f-i_i+i-i4-r_ etc. — l 



(B) I- 1-+-0+1 — i + o + i- I-I-0+ etc. =: j 



(A)-h(B) 2-2_-t-i + o+o~i + 2-2+i+ etc.zrl. 



Notetur nunc aggregntum cx \traque (cric ro- 

 vam fbrmare fcriem rccurrentem , in qua quacuis 

 periodus confhu cx fex terminis , poft quos con(^an- 

 tcr cadem rcfUrgit. lam \ero fi (crics in primo 

 pcriodi termino terminari ccnfcatur, erit lumma - 2 ,• 

 fi in fccundo fit fumma m o; i\ in tertio , erit 

 fumma — i eadcmquc crit fumma fi in quarto vel 

 in quinto tcrmino ferics tcrminctur atquc tnndcm 

 (\3mma crit — o , fi in \ltimo pcriodi tcrmino fc- 

 rics abrupta putctur ; funt igitur duo cafus , qui- 

 bus fumma fit — o; dein tres cafus , quibus fit ri 

 ct Ynus cafus , qui (ummam facit — z-^ liinc doce- 

 mur , ex lcge probabilitatum , fummam fcrici 2 — a 

 H- i 4-0-I-0 — I -f- 2 — 2-f- 1 4-ctc. flatucndam cfle 

 ■zz I plane vt prouidebatur. 



Simili modo , fi ferics (B) ab fcrie A fubtra- 

 hatur , ferics noua fexti ordinis oritur , cuius fingu- 

 Jae pcrioJi confbnt ex tcrminis o—o+i — 2 + 2-1 

 ct cuius fumma prouidctur rr l. Rcucra fumma 

 cft \cl o \cl o vel i \cl — I \el o, prouti fcrics 



\cl 



