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China Team Selection Test
2021 China Team Selection Test
4
maximum of sum of xi^2(x(i+1)-x(i-1))
maximum of sum of xi^2(x(i+1)-x(i-1))
Source: 2021ChinaTST test4 day2 P1
April 14, 2021
Inequality
algebra
TST
Problem Statement
Suppose
x
1
,
x
2
,
.
.
.
,
x
60
∈
[
−
1
,
1
]
x_1,x_2,...,x_{60}\in [-1,1]
x
1
,
x
2
,
...
,
x
60
∈
[
−
1
,
1
]
, find the maximum of
∑
i
=
1
60
x
i
2
(
x
i
+
1
−
x
i
−
1
)
,
\sum_{i=1}^{60}x_i^2(x_{i+1}-x_{i-1}),
i
=
1
∑
60
x
i
2
(
x
i
+
1
−
x
i
−
1
)
,
where
x
i
+
60
=
x
i
x_{i+60}=x_i
x
i
+
60
=
x
i
.
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