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Poland Contests
Polish MO Finals
1995 Polish MO Finals
1
given harmonic mean find minimum
given harmonic mean find minimum
Source: Problem 4, Polish NO 1995
October 21, 2005
inequalities unsolved
inequalities
Problem Statement
The positive reals
x
1
,
x
2
,
.
.
.
,
x
n
x_1, x_2, ... , x_n
x
1
,
x
2
,
...
,
x
n
have harmonic mean
1
1
1
. Find the smallest possible value of
x
1
+
x
2
2
2
+
x
3
3
3
+
.
.
.
+
x
n
n
n
x_1 + \frac{x_2 ^2}{2} + \frac{x_3 ^3}{3} + ... + \frac{x_n ^n}{n}
x
1
+
2
x
2
2
+
3
x
3
3
+
...
+
n
x
n
n
.
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