I am studying for my 2nd midterm, but then I am stuck..plz help me..thank you so much.

1) prove by induction that for each nonnegative integer k, the integer k^2 + 5k is even.

2) The number n!, which is the number of permutations of the first n positive integers, is defined recursively by 0! = 1 and n! = n X (n-1)! for all n > o. Prove that n! < n ^n for all n > 0 and strict inequality holds if n > 1.