Question 123
Prove that a sequence $(a_n)_{n \ge 1}$ having the property:
$$
a_n - \frac{1}{m} \le a_m \le \frac{m}{n}
$$
for all $m, n \in \mathbb{N}^*, m \ge n$, is convergent.
$$
a_n - \frac{1}{m} \le a_m \le \frac{m}{n}
$$
for all $m, n \in \mathbb{N}^*, m \ge n$, is convergent.