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7
2017 Algebra/NT #7: Largest number C satisfying Inequality
2017 Algebra/NT #7: Largest number C satisfying Inequality
Source:
February 19, 2017
inequalities
Problem Statement
Determine the largest real number
c
c
c
such that for any
2017
2017
2017
real numbers
x
1
,
x
2
,
…
,
x
2017
x_1, x_2, \dots, x_{2017}
x
1
,
x
2
,
…
,
x
2017
, the inequality
∑
i
=
1
2016
x
i
(
x
i
+
x
i
+
1
)
≥
c
⋅
x
2017
2
\sum_{i=1}^{2016}x_i(x_i+x_{i+1})\ge c\cdot x^2_{2017}
i
=
1
∑
2016
x
i
(
x
i
+
x
i
+
1
)
≥
c
⋅
x
2017
2
holds.
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