证明:(n+1)!/k!-n!/(k-1)!=(n-k+1)*n!/k!(k≤n)

问题描述:

证明:(n+1)!/k!-n!/(k-1)!=(n-k+1)*n!/k!(k≤n)

略证:
(n+1)!/k!-n!/(k-1)!
=(n+1)×(n!)/k! - n!/(k-1)!
=[(n+1)×(n!) - k×n!]/k!
=(n-k+1)×n!/k!