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Problems
Contests
National and Regional Contests
China Contests
China Team Selection Test
2024 China Team Selection Test
11
11
Part of
2024 China Team Selection Test
Problems
(1)
Writing numbers on a blackboard
Source: 2024 CTST P11
3/12/2024
There is number
1
1
1
on the blackboard initially. The first step is to erase
1
1
1
and write two nonnegative reals whose sum is
1
1
1
. Call the smaller number of the two
L
2
L_2
L
2
. For integer
k
≥
2
k \ge 2
k
≥
2
, the
k
{k}
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
k+1
k
+
1
on the blackboard
L
k
+
1
L_{k+1}
L
k
+
1
. Find the maximum of
L
2
+
L
3
+
⋯
+
L
2024
L_2+L_3+\cdots+L_{2024}
L
2
+
L
3
+
⋯
+
L
2024
.
combinatorics