Question 126
Let the sequence $a_1, a_2, \dots, a_n$ be such that $a_1 = 0$, $|a_2| = |a_1 + 1|$, $|a_3| = |a_2 + 1|$, $\dots$, $|a_n| = |a_{n-1} + 1|$. Prove that
$$
\frac{a_1 + a_2 + \dots + a_n}{n} \geq -\frac{1}{2}.
$$
$$
\frac{a_1 + a_2 + \dots + a_n}{n} \geq -\frac{1}{2}.
$$