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Swedish Mathematical Competition
1999 Swedish Mathematical Competition
5
x_1x_2 + x_2x_3 + ... + x_{n-1}x_n <= s^2/4
x_1x_2 + x_2x_3 + ... + x_{n-1}x_n <= s^2/4
Source: 1999 Swedish Mathematical Competition p5
April 2, 2021
inequalities
algebra
Problem Statement
x
i
x_i
x
i
are non-negative reals.
x
1
+
x
2
+
.
.
.
+
x
n
=
s
x_1 + x_2 + ...+ x_n = s
x
1
+
x
2
+
...
+
x
n
=
s
. Show that
x
1
x
2
+
x
2
x
3
+
.
.
.
+
x
n
−
1
x
n
≤
s
2
4
x_1x_2 + x_2x_3 + ... + x_{n-1}x_n \le \frac{s^2}{4}
x
1
x
2
+
x
2
x
3
+
...
+
x
n
−
1
x
n
≤
4
s
2
.
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