How do you proof that:

1. Show that f(n) is O(g(n)) if and only if g(n) is $\displaystyle \Omega(f(n))$

2. Show that $\displaystyle n^2$ is $\displaystyle \omega (n)$

3. $\displaystyle \sum_{i = 1}^n i^2$ is $\displaystyle O(n^3)$

I am really confused on doing this, can someone help me