112 Opdscula. 



praebet diffcrcnlias primi ordinis 



3, 5, 7, 11 eic. 

 diflerenlias secuodl ordinis 



2, 2, 2, 2 etc. 



. . 1 3 2 

 quae constantes sunli ergo crit summa senci-r H — r=^^- 



i2 4 b 



Qiiarlae seriei 



1 _ 8 4- 27 —64 + 125 — 216 



diflferentlae primi ordinis sunt 



7, 19, 37, 61, 91 etc. 



sccundi ordinis 



12,18,21,30 etc. 



lertii ordinis 6, 6, 6 etc. quae conslantcs sunt: summa ergo 



. 1 7 12 6 2 



quarlae seriei enl -—^+~ -- = -;^-Q . 



Qaintae seriei 



^ 1—16 4-81— 256 + 625 — 1296 etc. 



differentiae primi ordinis sunt 



15,65, 175, 369, 671 etc. 



secundi ordinis 



50, 110,194,302 etc. 



tcrlii ordinis 



60, 84, 103 etc. 



quarli ordinis 



24,24, etc. 



quae constantes sunl^ summa ergo quintae seriei erit 

 1 15 50 60 ^t__» 

 T'~~4'^'S "16 ■^"32" 



etc. etc. 



Ad detegendam autem summam seriei generalis i — 2" 

 ^,3n — 4"_j-5" etc. metliodo exposita,invenio differentias ipsius, 

 et erit, series differentiarum primi ordinis 



2u— 1 , 3n— 2" , 40— 3n , 50— 4" , 6n— 5n , 7"— S" , etc. 

 secundi ordinis 

 3n_2.2n4-l,4'»— 2.3n4.2'»,5°— 2.4n4-3n,6n— 2.5n4-4n,7n— 2.6M-5°> etc* 



lertii ordinis 



4n_3.3n_^3.9n_1,5'»— 3.4°-t-3.3«>— 2»,6»— 3.5«4-3.4»— 3fc, 



7n4-3.6n-h3.5n— 4'> etc. 



