MathDB
Problems
Contests
National and Regional Contests
North Macedonia Contests
Macedonian TST for the Balkan MO
2021 Macedonian Balkan MO TST
Problem 3
Upper bound for sum of k-th roots
Upper bound for sum of k-th roots
Source: 2021 Macedonian Balkan MO TST - Problem 3
August 18, 2021
inequalities
Problem Statement
Suppose that
a
1
,
a
2
,
…
a
2021
a_1, a_2, \dots a_{2021}
a
1
,
a
2
,
…
a
2021
are non-negative numbers such that
∑
k
=
1
2021
a
k
=
1
\sum_{k=1}^{2021} a_k=1
∑
k
=
1
2021
a
k
=
1
. Prove that
∑
k
=
1
2021
a
1
a
2
…
a
k
k
≤
3.
\sum_{k=1}^{2021}\sqrt[k]{a_1 a_2\dots a_k} \leq 3.
k
=
1
∑
2021
k
a
1
a
2
…
a
k
≤
3.
Back to Problems
View on AoPS