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1991 Baltic Way
5
Inequality involving harmonic sums
Inequality involving harmonic sums
Source:
April 19, 2013
inequalities
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Problem Statement
For any positive numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
prove the inequalities
1
a
+
1
b
+
1
c
≥
2
a
+
b
+
2
b
+
c
+
2
c
+
a
≥
9
a
+
b
+
c
.
\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge \frac{2}{a+b}+\frac{2}{b+c}+\frac{2}{c+a}\ge \frac{9}{a+b+c}.
a
1
+
b
1
+
c
1
≥
a
+
b
2
+
b
+
c
2
+
c
+
a
2
≥
a
+
b
+
c
9
.
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