ALGEBRA. 39 



187. Prove that 



/ IN / I \ / ft\ 



! = [2~" ~~DT~ 



n(tt-l)(n-2)(n-3) 



f O r-j ... 



188. Prove that 



(1 + r 4-r 1 + r s )(l + r' + r 4 



189. Prove that 



n-1 (n-2)(n-3) 



'"" ~~ 



f2 



190. Prove that ' ^ -/- f^<^ J f J/ 



t n(n4-l) n(n + l)(n + 2) 



~ "~ 



li 



*!)(+ 2). ..2/ 

 - - . . 

 |n 



191. Prove that 



1 1.3 1 



1 , 



m -f n (w -- n) (m + ;t - 1 ) 



m (m - 1 ) . 1 



r-. -- . .. to w + 1 terms = , 

 - 1) n 



m (m + 1) ^ m 



m+p (m+p)(m+p+l) p- 



bcing any positive quantity > 1. 



