" 6.Prove that "n!(n+2)=n!+(n+1)!

Prove that n! + (n + 1)! = n! (n + 2)

For n in N , Prove that (n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!

Prove that n(n-1)(n-2) ...(n-r+1)=(n!)/((n-r)!).

For a fixed positive integer n prove that: D = |[n!, (n+1)!, (n+2)!],[(n+1)!,(n+2)!,(n+3)!],[(n+2)!,(n+3)!,(n+4)!]|= ( n !)^3(2n^3+8n^2+10n+4 )

For n in N, prove that (n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!

16.Prove that (x^(n))/(n)!+(x^(n-1)*a)/((n-1)!1!)+(x^(n-2)*a^(2))/((n-2)!2!)......+(a^(n))/(n!)=((x+a)^(n))/(n!)

Prove that [n+1/2]^(n)>(n!)

Prove that : 1+2+3++n=(n(n+1))/2

Prove that: n(n-1)(n-2)…..(n-r+1)=(n!)/((n-r)!)

Prove that ((2n+1)!)/(n!)=2^(n){1.3.5(2n-1)(2n+1)}