Dots, ka \(0 \leq a_{1} \leq a_{2} \leq \cdots \leq a_{1000}\) un \(a_{1}+a_{2}+\cdots+a_{1000}=1\). Pierādīt, ja \(n\) ir naturāls skaitlis un \(1 \leq n \leq 1000\), tad \(\frac{a_{1}+a_{2}+\cdots+a_{n}}{n} \leq \frac{1}{1000}\)