MathNet 2009-part-01 — 175 problems (EN–VI) Question 28

Let $n$ be a given positive integer. Show that we can choose numbers $c_{k} \in \{-1,1\}$ $(1 \leq k \leq n)$ such that
$$
0 \leq \sum_{k=1}^{n} c_{k} \cdot k^{2} \leq 4
$$