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Baltic Way
2000 Baltic Way
19
n-th power inequality for the real t
n-th power inequality for the real t
Source: Baltic Way 2000
December 17, 2010
inequalities
algebra proposed
algebra
Problem Statement
Let
t
≥
1
2
t\ge\frac{1}{2}
t
≥
2
1
be a real number and
n
n
n
a positive integer. Prove that
t
2
n
≥
(
t
−
1
)
2
n
+
(
2
t
−
1
)
n
t^{2n}\ge (t-1)^{2n}+(2t-1)^n
t
2
n
≥
(
t
−
1
)
2
n
+
(
2
t
−
1
)
n
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