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National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2003 Switzerland Team Selection Test
3
3
Part of
2003 Switzerland Team Selection Test
Problems
(1)
Infimum and supremum for an expression
Source: Swiss IMO TST 2003
2/27/2014
Find the largest real number
C
1
C_1
C
1
and the smallest real number
C
2
C_2
C
2
, such that, for all reals
a
,
b
,
c
,
d
,
e
a,b,c,d,e
a
,
b
,
c
,
d
,
e
, we have
C
1
<
a
a
+
b
+
b
b
+
c
+
c
c
+
d
+
d
d
+
e
+
e
e
+
a
<
C
2
C_1 < \frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+d}+\frac{d}{d+e}+\frac{e}{e+a} < C_2
C
1
<
a
+
b
a
+
b
+
c
b
+
c
+
d
c
+
d
+
e
d
+
e
+
a
e
<
C
2
inequalities proposed
inequalities