328 NEW SERIES for the 
ter tran{pofing, we get 
"i x+r 
x—I 
Ir I I I 
2 4 t To 
x —I x —tI x —I xX ——I 
im ' I I I I 
x +1 a r + - E + 3 1 + 6 ° 
z = “x +1 x +I x +I x +r 
m (x — 1) é 
m 
| —I 
I 
| += —— 
l x +1 
THIs equation, which is identical, holds true whatever be 
the value of 7. Let us now, however, fuppofe, that # is inde- 
finitely great, then the feries will go on ad infinitum, and 
m = 2” will become indefinitely great; but this being the cafe, 
will 
I 
Pas id 
I 
become fimply 2; and m (e* — 1) will become Nap. log x, 
(Art. 57.) ; therefore eee eatia) thefe limits, and cing by 
2, we have 
Ix+I 
2X —--1 
1 a uf 
t? — ' wen a 
I sit ak dtl at a I 
~—+37—-+3——-+5 +, 
x? +1 xt +t we +1 3 wie ty 
and 
