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National and Regional Contests
China Contests
(China) National High School Mathematics League
2021 China Second Round A2
3
inequality in 2021 China Second Round A2
inequality in 2021 China Second Round A2
Source: 2021 China Second Round A2
February 20, 2023
inequalities
Problem Statement
Given
n
≥
2
n\geq 2
n
≥
2
,
a
1
a_1
a
1
,
a
2
a_2
a
2
,
⋯
\cdots
⋯
,
a
n
∈
R
a_n\in\mathbb {R}
a
n
∈
R
satisfy
a
1
⩾
a
2
⩾
⋯
⩾
a
n
⩾
0
,
a
1
+
a
2
+
⋯
+
a
n
=
n
.
a_1\geqslant a_2\geqslant \cdots \geqslant a_n\geqslant 0,a_1+a_2+\cdots +a_n=n.
a
1
⩾
a
2
⩾
⋯
⩾
a
n
⩾
0
,
a
1
+
a
2
+
⋯
+
a
n
=
n
.
Find the minimum value of
a
1
+
a
1
a
2
+
⋯
+
a
1
a
2
⋯
a
n
a_1+a_1a_2+\cdots +a_1a_2\cdots a_n
a
1
+
a
1
a
2
+
⋯
+
a
1
a
2
⋯
a
n
.
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