Question 20
Let $n$ be a positive integer and let $a_{1}, a_{2}, \ldots, a_{n}$ be any real numbers. Prove that there exist $m, k \in \{1,2, \ldots, n\}$ such that
$$
\left|\sum_{i=1}^{m} a_{i}-\sum_{i=m+1}^{n} a_{i}\right| \leq\left|a_{k}\right| .
$$
$$
\left|\sum_{i=1}^{m} a_{i}-\sum_{i=m+1}^{n} a_{i}\right| \leq\left|a_{k}\right| .
$$