328 NEW SERIES for the 



ter tranfpofing, we get 



x-\- 1 



x -f- I 



m(x — i) 



x 



X 



X — I 



X 



X 



16 



<l- 



+ l .-T 



4 4 



+ 1 



< 



X ■+• I 



* +1 



8 1 



8 . 

 * + I 



+ A 



16 -. 



i<5 

 X -f- I 



+ 



I 

 X l\ 



/» / 



This equation, which is identical, holds true whatever be 

 the value of n. Let us now, however, fuppofe, that n is inde- 

 finitely great, then the feries will go on ad infinitum, and 

 m zz 2 !l will become indefinitely great \ but this being the cafe, 



»+ i> which is always lefs than 2 -f- :, (Art. 53«)> will 



X TJl 



become limply 2 ; and m (x ' — i) will become Nap. log x, 



(Art. 57.) ; therefore fubftituting thefe limits, and dividing by 

 2, we have 



r ix-f-i 

 2 # ~i 



log X 







a: 8 — 1 



+ ^-^+l 



x iZ — 1 



&c.) 



16 



X Y -f-I 



O* v 1 i 



-f, 



ff ,7 +I 



and 



