Prove that if n ∈ ℕ where n > 1, then n + 1 is odd.

[Dustinsfl]

Prove that if n ∈ ℕ where n > 1, then n! + 1 is odd.
n = k + 1, k = 1,...,∞
Now substitute n!+1 = (k+1)! + 1 = ?

I am not sure what to do next or if that is on the right path.

 

[snipez90]

If n > 1 then n! is an even number since it has 2 as one of its factors, so n! is even for n > 1. Conclude.