Prove that the following inequalities f(n) ≤ g(n) hold “for sufficiently large n.” That is, identify an integer k and then prove (by induction on n) that f(n) ≤ g(n) for all integers n ≥ k 1.2 n ≤ n!...

Prove that the following inequalities f(n) ≤ g(n) hold “for sufficiently large n.” That is, identify an integer k and then prove (by induction on n) that f(n) ≤ g(n) for all integers n ≥ k

1.2 n ≤ n!

2. n ≤ n!, for an arbitrary integer b ≥ 1

3. 3n ≤ n2

4. n3 ≤ 2