332 NEW SERIES for the 



the refult, after tranfpofition, will be 



' IX + Ty 



(x m + i)' 



m (x — I ) 



= S 



V* 1/ v 2 2.4 2.4 2.4 3 2.4" -l/ 



1 I £ 



f ? 4 s 



\ t /* "~ * V T ,x — I X — I 



x f 1 



4 , 

 x -f i 



x° -f 1 



+ 





1 

 x 4- 1 



This equation holds true when n is any whole pofitive number 

 whatever. But if we fuppofe it indefinitely great, then the two 

 feries will go on ad infinitum, and the limit of the numerical fe- 



ries will be 2, a lfo the limit of (*'" + i)* will be 4, and the li- 



T 



mit of wp- (x m — i)* will be log**, (Art. 57.) ; therefore, fub- 



llituting thefe limits, and alfo putting 4* _j_ i f Qr 



( x ~* J ) 2 3 



VJb^i) — |» and dividing the whole expreffion by 4, we 

 get 



log'* 



