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2017 CMIMC Algebra
2
2017 A2: Iterated Function
2017 A2: Iterated Function
Source:
January 29, 2017
2017
algebra
function
Problem Statement
For nonzero real numbers
x
x
x
and
y
y
y
, define
x
∘
y
=
x
y
x
+
y
x\circ y = \tfrac{xy}{x+y}
x
∘
y
=
x
+
y
x
y
. Compute
2
1
∘
(
2
2
∘
(
2
3
∘
⋯
∘
(
2
2016
∘
2
2017
)
)
)
.
2^1\circ \left(2^2\circ \left(2^3\circ\cdots\circ\left(2^{2016}\circ 2^{2017}\right)\right)\right).
2
1
∘
(
2
2
∘
(
2
3
∘
⋯
∘
(
2
2016
∘
2
2017
)
)
)
.
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