(IIP)== 



vata hac lege facile erit fradiones partiales producerc qiious- 

 que libuerit , et fummae ferierum hoc modo commodius de 

 tegi poflc videntur. 



Inanem operam fidlurus cfTem, fi fummationcs has vl- 

 terius producere vellem ; minime tamen praetcreundum effe 

 videtur fimilem in modum feries poteftatum numerorum im- 

 porium alternis fignis aflfecftarum fummari pofle. Sit feries fum- 

 menda in genere 



I — 3"-f-5'' — ^''-l-p'' — ii"-f- etc. 

 in qua, fi ponatur « rz: i, prodibit feries, cuius fumma quac- 

 renda efl: 



I — 34-5 — 7-1-9 — 11-I-13 — etc. 

 Statuatur : 



j =: I — sxx -h 5 x'* — 7 jf* H- 9 jf* — 1 1 jf" -I- etc. 

 Ducendo in dx et fumendo integrali habebimus: 



fsd X z=z X — jr^ -h >v^ — x^ -h^' — *"" -H etc. 



fiue 



fs^dx — X (i — j^jf H-j^^— jc*-4-x' — .v'°-+- etc.) =r - 



Differentiando igitur et per dx diuidendo reperitur s zz 

 ac pofito jr r= I, fumma feriei quaefitae prodit m o. 



CafuS II. quo eft « zz: 2 et feries fummanda 



I — 3'-l-5"-— 7'H-9"'— n"--f- etc. 

 Ponamus 



/^ =r I — 3- JT A- -+- 5* X* — 7^ jr^ -+- 9- ;c' — II* x'^ -f- etc. 

 Hinc 



/-'^jr — dx— Hi^-xxdx-^^^^x^dx—^^-x^^dx-^g-x^dx-- ctc. 

 ac 



fs^^dx~x (i— 3Jf jr-+- $ x^ ■— '^ x^ -{- 9 x* ■— iijc"-4- etc.) 



Eft 



■ X 36 

 I X X ' 



(1 -(-XJC)*' 



