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Contest of the Centers of Excellency of Suceava
2019 Centers of Excellency of Suceava
1
Combinatoric AM-GM
Combinatoric AM-GM
Source:
July 7, 2020
inequalities
AM-GM
Problem Statement
Prove that
(
m
+
n
min
(
m
,
n
)
)
≤
(
2
m
m
)
⋅
(
2
n
n
)
,
\binom{m+n}{\min (m,n)}\le \sqrt{\binom{2m}{m}\cdot \binom{2n}{n}} ,
(
m
i
n
(
m
,
n
)
m
+
n
)
≤
(
m
2
m
)
⋅
(
n
2
n
)
,
for nonnegative
m
,
n
.
m,n.
m
,
n
.
Gheorghe Stoica
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