MathDB
Problems
Contests
Undergraduate contests
IMS
2006 IMS
1
Sum
Sum
Source: IMS 2006
July 14, 2006
inequalities
combinatorics proposed
combinatorics
Problem Statement
Prove that for each
m
≥
1
m\geq1
m
≥
1
:
∑
∣
k
∣
<
m
(
2
m
m
+
k
)
≥
2
2
m
−
1
\sum_{|k|<\sqrt m}\binom{2m}{m+k}\geq 2^{2m-1}
∣
k
∣
<
m
∑
(
m
+
k
2
m
)
≥
2
2
m
−
1
[hide="Hint"]Maybe probabilistic method works
Back to Problems
View on AoPS