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

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

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)!

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

Prove that : ^(2n)C_n = (2^n [1.3.5. ..........(2n-1)])/(n!) .

Prove that : (2n) ! = 2^n (n!)[1.3.5.... (2n-1)] for all natural numbers n.

Prove that 2^(n)>n,n in N

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

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

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