MathDB
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Contests
National and Regional Contests
Mongolia Contests
Mongolia Team Selection Test
2011 Mongolia Team Selection Test
1
Mongolia TST 2011 Test 4 #1
Mongolia TST 2011 Test 4 #1
Source: Mongolia TST 2011 Test 4 #1
November 8, 2011
inequalities unsolved
inequalities
Problem Statement
Let
t
,
k
,
m
t,k,m
t
,
k
,
m
be positive integers and
t
>
k
m
t>\sqrt{km}
t
>
km
. Prove that
(
2
m
0
)
+
(
2
m
1
)
+
⋯
+
(
2
m
m
−
t
−
1
)
<
2
2
m
2
k
\dbinom{2m}{0}+\dbinom{2m}{1}+\cdots+\dbinom{2m}{m-t-1}<\dfrac{2^{2m}}{2k}
(
0
2
m
)
+
(
1
2
m
)
+
⋯
+
(
m
−
t
−
1
2
m
)
<
2
k
2
2
m
(proposed by B. Amarsanaa, folklore)
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