ALGEBRA. 

 prove that the limit of ~ when n is indefinitely increased U 



182. If there be a series of terms , w,, u f u a ... t*...., of 

 which any one is obtained from the preceding by the formula 



u m = nu m _i + (_!)", and if U Q = 1 ; then wi 

 ( n(n-l) u + ?t?-Jl 



Prove also that ^ tends to become equal to-, as n is in den 



[n 



nit"ly increased. 



183. Prove that 



2-" -2 _ 2 . _ n-l 2 ._, + (n- 2) (n -3) ^ _ 



and that 



n(n-3) 

 P + 9 = (P + ?) - rc(/> + 7)" f />7 -f r^ 



_n(n^4)(n-g) (>> ^ r ., ffy ^ 

 l 



184. By means of tin- identity 



log(l-V)=log(l-*)+log(l 

 prove that 



._. 3n(3n + l) (3n- 1) 3n(3n4- 1) (3n + 2) 



"js~ \ir 



the series being carried to 3n terms. 



185. If there be n quantities a, 6, c, ... and $ m 



ir .sum, 8 n _ t the sum ot any n - 1 of them, and to on, and if 



- 



