200 Analytical Theorems relating to Geometrical Series, 



X . , 



X &c. &c. &c. 





Dem, 



^ ^jP »P ^ ,^ n^nP 



By Art. 1 



= ^|l-,.4.^2_g^^ ^m-2^^,m--iy\ 



By dividing each side of the equation by l—r + r^-&c. 



'm—2 . m—l 



.... — r -\-r 



we get — 



Dividing each side by l-r^ + r^'^ y(»— ^j^^/m-^a 



we have 





and by performing the division in like manner q times, we 

 have at length 



