332 NEW SERIES for the 
the refult, after tranfpofition, will be 
apie kee 2 ct Se 
24 24° 2.45 2.47—* 
Cee “ft ee 
ae te socsoudeay 
r hoa C ae ae oa Bs dae 
m* (x" —1)° | ‘ 
: 
This Soke holds true when 2 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, alfo the limit of (#"+-') ‘will be'4; and tHeli+ 
mit of m(x”—1)° will be log, (Art. 57.) ; therefore, fub- 
ftituting thefe limits, and alfo putting —4* 4+ for 
@ =a) 
=a) = , and dividing the whole expreflion by 4, we 
get i 
Tt — 
log’ * ~~ 
