f + /^ + /j + 4f -4- ^ 4- lio + etc. zz: r - / 2. 

 Aequalitas quae intcr has ambas feries prorfus fingulares fub- 

 fiftit, inducit me pofterioris dcmonllrationem diredam hcic ap- 

 ponere, ex qua fimul ordo denominatorum aliquanto clarius 

 perfpicictur quam quidem eum ex diflertatione citata intelii- 

 gere licet. 



Theorema III. 



§. 2 2. Si omnes potejlates impares 



9, 25, 2-7, 49, 81, 121, 125, 169, 225, etc. 



vtiltate minuantur^ indeque formetur haec feries reciprocai 



J -+- 5:1 -f- J5 -4- 4g -H jo -+- 150 -^ 124 "+" i?s "^ etc. 

 tius fumma erit i — l 2. 



Demonflratio. 



Confideretur haec feries reciproca numerorum impa- 



rium : 



X =1 I -+- 1 -f- 1 -+- 1 -+- J -+- /7 -t- 1\ -+- etc. 



ct cum fit 



-^ = i + ^ + ---{--, -f- -1 -4- etc. 



fumto « 1= 3 erit 



1 1 _(_ I _J ^ |_ 1 I I 1_ af-f 



2 3 ^ 9 ^ 27 ^ 81 ^ 343 • Cll,. 



qua ferie ab illa ablata expulfi erunt omnes denominatores 

 formae 3'', hoc eft termini |, i, /^, etc. ita vt remaneat: 



X — l =: I -*- 1 -+- j -h {j -i~ i-^ -i- /5 -+- /7 H- etc. 



Eodem modo, fumto « — 5, fit 



J = f -+- 55 -^ I5S -+- etc. 



E c 3 qua 



