why a Bezier curve is guaranteed to lie within the convex hull of its control points?

why if Bernstein basis polynomials are non-negative ($$B_{k,n}(x) \geq 0$$) and also due to the Partition of Unity/sum up to one ($$\sum_{k=0}^n B_{k,n}(x) = 1, for\ all\ x \in [0,1]$$) implies Bezier curve is guaranteed to lie within the convex hull of its control points $$CH=(\{p_{0},p_{1},p_{2},...,p_{n}\})$$

• A convex combination of the points $$p_{0},p_{1},p_{2},...,p_{n}$$ is a point of the form $$\sum_{k=0}^n \lambda_k p_k$$. where $$\lambda_k \ge 0$$ and $$\sum_{k=0}^n \lambda_k = 1$$.
• The convex hull of the points $$p_{0},p_{1},p_{2},...,p_{n}$$ is the set of all convex combination of $$p_{0},p_{1},p_{2},...,p_{n}$$.