Question 5
Given non-negative real numbers $a_1$, $a_2$, ..., $a_n$, such that $a_{i-1} \leq a_i \leq 2a_{i-1}$ for $i = 2, 3, \ldots, n$. Show that you can form a sum $s = b_1 a_1 + \ldots + b_n a_n$ with each $b_i = +1$ or $-1$, so that $0 \leq s \leq a_1$.