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A2
Maximal value
Maximal value
Source: 2022 IMOC A2
September 5, 2022
inequalities
Problem Statement
Given positive integer
n
>
2
,
n>2,
n
>
2
,
consider real numbers
a
1
,
a
2
,
…
,
a
n
a_1,a_2,\dots, a_n
a
1
,
a
2
,
…
,
a
n
satisfying
a
1
2
+
a
2
2
+
…
a
n
2
=
1.
a^{2}_1+a^2_2+\dots a^2_n=1.
a
1
2
+
a
2
2
+
…
a
n
2
=
1.
Find the maximal value of
∣
a
1
−
a
2
∣
+
∣
a
2
−
a
3
∣
+
⋯
+
∣
a
n
−
a
1
∣
.
|a_1-a_2|+|a_2-a_3| +\dots +|a_n-a_1|.
∣
a
1
−
a
2
∣
+
∣
a
2
−
a
3
∣
+
⋯
+
∣
a
n
−
a
1
∣.
Proposed by ltf0501
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