MathDB
Problems
Contests
National and Regional Contests
Mathlinks Contests.
MathLinks Contest 3rd
3
0363 inequalities 3rd edition Round 6 p3
0363 inequalities 3rd edition Round 6 p3
Source:
May 9, 2021
inequalities
3rd edition
Problem Statement
Let
n
≥
3
n \ge 3
n
≥
3
be an integer. Find the minimal value of the real number
k
n
k_n
k
n
such that for all positive numbers
x
1
,
x
2
,
.
.
.
,
x
n
x_1, x_2, ..., x_n
x
1
,
x
2
,
...
,
x
n
with product
1
1
1
, we have
1
1
+
k
n
x
1
+
1
1
+
k
n
x
2
+
.
.
.
+
1
1
+
k
n
x
n
≤
n
−
1.
\frac{1}{\sqrt{1 + k_nx_1}}+\frac{1}{\sqrt{1 + k_nx_2}}+ ... + \frac{1}{\sqrt{1 + k_nx_n}} \le n - 1.
1
+
k
n
x
1
1
+
1
+
k
n
x
2
1
+
...
+
1
+
k
n
x
n
1
≤
n
−
1.
Back to Problems
View on AoPS