Given a sequence of vectors $(a_1, 1), \cdots, (a_i, 1), \cdots, (a_n, 1)$ such that $ a_i \in \mathbb{R}^+$.
And my interest is to find extreme points(extreme points of the convex hull) of the cumulative sequence $B = (\sum_{i=1}^1 a_i, \sum_{i=1}^1 1), \cdots, (\sum_{i=1}^j a_i, \sum_{i=1}^j 1), \cdots, (\sum_{i=1}^n a_i, \sum_{i=1}^n 1)$.
And my hypothesis is: suppose $a_k = max(\{a_1, \cdots, a_i, \cdots, a_n\})$, then $b_k$ must be extreme points of $CH(B)$.
Is this a valid claim?
If so, can I apply this method in a recursive fashion separate the $A$ into $A_1, A_k$ and $A_k, A_n$ and apply similar argument to obtain the upper hull of $B$ ?