IMC 2021 Problem 3

We say that a positive real number $d$ is $good$ if there exists an infinite squence $a_1,a_2,a_3,...\in (0,d)$ such that for each $n$ , the points $a_1,a_2,...,a_n$ partition the interval $[0,d]$ into segments of length at most $\frac{1}{n}$ each . Find $\text{sup}\{d| d \text{is good}\}$ .