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All-Russian Olympiad Regional Round
2005 All-Russian Olympiad Regional Round
10.2
Inequlity by Khrabrov
Inequlity by Khrabrov
Source: All-Russian MO Round 4, 2005
April 2, 2005
inequalities
inequalities proposed
Problem Statement
10.2 Prove for all
x
>
0
x>0
x
>
0
and
n
∈
N
n\in\mathbb{N}
n
∈
N
the following inequality
1
+
x
n
+
1
≥
(
2
x
)
n
(
1
+
x
)
n
−
1
.
1+x^{n+1}\geq \frac{(2x)^n}{(1+x)^{n-1}}.
1
+
x
n
+
1
≥
(
1
+
x
)
n
−
1
(
2
x
)
n
.
(A. Khrabrov)
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