MathDB
Problems
Contests
National and Regional Contests
Finland Contests
Finnish National High School Mathematics Competition
2012 Finnish National High School Mathematics Competition
4
Combinatorial Inequality
Combinatorial Inequality
Source: Finland 2012, Problem 4
May 5, 2013
inequalities
induction
combinatorics unsolved
combinatorics
Problem Statement
Let
k
,
n
∈
N
,
0
<
k
<
n
.
k,n\in\mathbb{N},0<k<n.
k
,
n
∈
N
,
0
<
k
<
n
.
Prove that
∑
j
=
1
k
(
n
j
)
=
(
n
1
)
+
(
n
2
)
+
…
+
(
n
k
)
≤
n
k
.
\sum_{j=1}^k\binom{n}{j}=\binom{n}{1}+ \binom{n}{2}+\ldots + \binom{n}{k}\leq n^k.
j
=
1
∑
k
(
j
n
)
=
(
1
n
)
+
(
2
n
)
+
…
+
(
k
n
)
≤
n
k
.
Back to Problems
View on AoPS