Little-O: $\forall c \in \mathbb{R^+}, \exists n_0 \in \mathbb{R^+}, \forall n \in \mathbb{N}, n ≥ n_0 ⇒ g(n) \leq cf(n)$
For positive functions $f,g\colon \mathbb{N} \to \mathbb{R}_+$, you can show that


$f(n) = o(g(n))$ iff $\lim_{n\to\infty} \frac{f(n)}{g(n)} = 0$.
$f(n) = O(g(n))$ iff $\limsup_{n\to\infty} \frac{f(n)}{g(n)} &lt; \infty$.


Using this, it is not hard to prove the two statements. Once you have done that, try translating your proofs to the definitions you were given.