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Rioplatense Mathematical Olympiad, Level 3
1997 Rioplatense Mathematical Olympiad, Level 3
5
5
Part of
1997 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
max of x_1x_2 + x_2x_3 + ... + x_{n-1}x_n if sum x_1=1, x_1>0
Source: VI - Rioplatense 1997 L3 P5
9/19/2022
Let
x
1
,
x
2
,
.
.
.
,
x
n
x_1, x_2, ... , x_n
x
1
,
x
2
,
...
,
x
n
be non-negative numbers
n
≥
3
n\ge3
n
≥
3
such that
x
1
+
x
2
+
.
.
.
+
x
n
=
1
x_1 + x_2 + ... + x_n = 1
x
1
+
x
2
+
...
+
x
n
=
1
. Determine the maximum possible value of the expression
x
1
x
2
+
x
2
x
3
+
.
.
.
+
x
n
−
1
x
n
x_1x_2 + x_2x_3 + ... + x_{n-1}x_n
x
1
x
2
+
x
2
x
3
+
...
+
x
n
−
1
x
n
.
algebra
inequalities