Problem

Source: 2024 CTST P11

Tags: combinatorics



There is number $1$ on the blackboard initially. The first step is to erase $1$ and write two nonnegative reals whose sum is $1$. Call the smaller number of the two $L_2$. For integer $k \ge 2$, the ${k}$ the step is to erase a number on the blackboard arbitrarily and write two nonnegative reals whose sum is the number erased just now. Call the smallest number of the $k+1$ on the blackboard $L_{k+1}$. Find the maximum of $L_2+L_3+\cdots+L_{2024}$.