Problem 275 (difficulty: 5/10)

Bizonyítsuk be, hogy tetszőleges \(\displaystyle a_1,a_2,\ldots\) valós számsorozatra

\(\displaystyle \liminf\frac{a_1+a_2+\ldots+a_n}{n} \ge \liminf a_n \quad\text{és}\quad \limsup\frac{a_1+a_2+\ldots+a_n}{n} \le \limsup a_n. \)

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