Proof of Binomial Theorem. 15 



It has now been shown that the limit of the series 



n 11 n — 1 n n — 1 n — 2 



1 ^ a- H . x" -\ . . x^ +. . . . 



1 12 1 2 3 - 



is (1 + ^)'* for all negative and fractional values of n, provided 



X be numerically less than one. For values of x greater than 



one, it is easy to show that the series is not convergent. In a^ 



elementary treatise it is not necessary to consider the case x = 1, 



since the only result would be to establish certain expressions 



for " and 2 " no use for which need arise in such a work. 





