ALGEDIiA. 37 



_ 

 U * = 



and S = 



1 (r + i;^ 1 



- (a - b) (a) (a + b) {a-f (r - 1)6}]. 



The sums of many series can also be expressed in a finite 

 form by equating the coefficients of x* in the expansions of the 

 same function of x effected by two different methods, of which 

 examples have been given in the Binomial, Exponential, and 

 Logarithmic Series. 



In the following examples, n always means a positive 

 number. 



186. Sum the series : 



135 2/*-l 



v ' F72 2. a 5.10 {1+ (-!)'} (!+*) 



(2) * , *-S-. + -L*lJU... 



1.3.5 



12 22* w.2" 



.2.3 + L4 + ...... + !1 





n 71 * 



n*!^* ...... 



