ALGEKKA. 



1G4. Tlic number of ways in which r things may bo di 



among n + p persons, so that certain n of those persons may 

 each have one at least, is (S r ) 



Hence prove that 



X. Binomial Tlieorem. 



1G.">. Prove that 



l + x n(n-l) 1 4- 2x 



n 



n(n-l)Jn-2) 1 4- 3x 

 ~~[3~ ' (l+nxf* 



n being a whole number. 



\ ' bermiM a, 6, c, ^ 6 in order that the n tt term in the 

 expansion of 



may 



I'r ..v.- :!i;it the scries 

 r + 2'* + 3 V + ...... 



is the expansion of a function of x of the t 



also prove that 



