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Balkan MO
1995 Balkan MO
1
Evaluate the expression
Evaluate the expression
Source: Balkan MO 1995, Problem 1
April 24, 2006
induction
algebra proposed
algebra
Problem Statement
For all real numbers
x
,
y
x,y
x
,
y
define
x
⋆
y
=
x
+
y
1
+
x
y
x\star y = \frac{ x+y}{ 1+xy}
x
⋆
y
=
1
+
x
y
x
+
y
. Evaluate the expression
(
⋯
(
(
(
2
⋆
3
)
⋆
4
)
⋆
5
)
⋆
⋯
)
⋆
1995.
( \cdots (((2 \star 3) \star 4) \star 5) \star \cdots ) \star 1995.
(
⋯
(((
2
⋆
3
)
⋆
4
)
⋆
5
)
⋆
⋯
)
⋆
1995.
Macedonia
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