RU-ALLRUSSIAN 1968 Problem 20

The sequence $\mathrm{a_1,a_2,\ldots,a_n}$ satisfies the following conditions: $\mathrm{a_1 = 0}$ $\mathrm{|a_i| = |a_{i - 1} + 1|}$ for $\mathrm{i} = 2$ , 3, ... , n. Prove that $(\mathrm{a_1 + a_2 + \ldots + a_n}) / \mathrm{n}\geq - 1 / 2$ .