Denumerable and Induction

If x > 1 is a given real number, then for every integer n > or equal to 2, (1 + x)^n > 1 + nx. .

I would be grateful if someone could show me how to prove by induction the attached formula. .

1. Show that if A and > are denumerable disjoint sets then A u > is denumerable

2. Show that every set of cardinalty c contains a denumerable subset

3. Show by induction that 6 divides n^3 - n for all n in N