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Bosnia Herzegovina Team Selection Test
2009 Bosnia Herzegovina Team Selection Test
3
Bosnia 2009 Problem 3
Bosnia 2009 Problem 3
Source:
August 10, 2010
inequalities proposed
inequalities
Problem Statement
a
1
,
a
2
,
…
,
a
100
a_{1},a_{2},\dots,a_{100}
a
1
,
a
2
,
…
,
a
100
are real numbers such that:
a
1
≥
a
2
≥
⋯
≥
a
100
≥
0
a_{1}\geq a_{2}\geq\dots\geq a_{100}\geq0
a
1
≥
a
2
≥
⋯
≥
a
100
≥
0
a
1
2
+
a
2
2
≥
100
a_{1}^{2}+a_{2}^{2}\geq100
a
1
2
+
a
2
2
≥
100
a
3
2
+
a
4
2
+
⋯
+
a
100
2
≥
100
a_{3}^{2}+a_{4}^{2}+\dots+a_{100}^{2}\geq100
a
3
2
+
a
4
2
+
⋯
+
a
100
2
≥
100
What is the minimum value of sum
a
1
+
a
2
+
⋯
+
a
100
.
a_{1}+a_{2}+\dots+a_{100}.
a
1
+
a
2
+
⋯
+
a
100
.
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