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

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

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

Use the Principle of Mathematical Induction to prove that n(n + 1) (2n + 1) is divisible by 6 for all n in N.

For an positive integer n, prove that : i^(n) + i^(n+1) + i^(n+2) + i^(n+3) + i^(n+4) + i^(n + 5) + i^(n+6) + i^(n+7) = 0 .

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

Prove, by Mathematical Induction, that for all n in N, n(n + 1) (n + 2) (n + 3) is a multiple of 24.

Prove that (n!)^2 le n^n. (n!)<(2n)! for all positive integers n.

Prove the following: sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x

Use method of induction, prove that : If n^3+(n+ 1)^3+(n+ 2)^3 is divisible by 9 for every n in N