RU-ALLRUSSIAN 1966 Problem 6

Given non- negative real numbers $\mathrm{a_1}$ , $\mathrm{a_2}$ , ..., $\mathrm{a_n}$ , such that $\mathrm{a_{i - 1}} \leq \mathrm{a_i} \leq 2\mathrm{a_{i - 1}}$ for $i = 2,3,\ldots ,\mathrm{n}$ . Show that you can form a sum $\mathrm{s} = \mathrm{b_1a_1} + \ldots +\mathrm{b_na_n}$ with each $\mathrm{b_i} + 1$ or - 1, so that $0 \leq \mathrm{s} \leq \mathrm{a_1}$ .