Prove that ncr/ncr-1=n-r+1/r
(nCr-1) = n! / (r-1)! ( n- (r-1))!
⇒ n! / (r-1)! (n-r+1)!
⇒ n! / (r-1)! (n-r)! (n-r+1).......................(1) and
⇒ nCr= n! / r! (n-r)!
⇒ n! / r (r-1)! (n-r)!.....................(2)
dividing (2) by (1) we get
nCr-1/ nCr= n-r+1/ r since other terms cancel out
Hence proved.