Prove that the number $1$ can be written as a sum of $2023$ fractions of the form $\frac{1}{k_i}$, where all nonnegative integers $k_i (1\leq i\leq 2023)$ are distinct.
Source: Moldova EGMO TST 2023
Tags: combinatorics
Prove that the number $1$ can be written as a sum of $2023$ fractions of the form $\frac{1}{k_i}$, where all nonnegative integers $k_i (1\leq i\leq 2023)$ are distinct.