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19
2000 Guts #19: Operation on integers
2000 Guts #19: Operation on integers
Source:
October 12, 2014
Problem Statement
Define
a
∗
b
=
a
−
b
1
−
a
b
a*b=\frac{a-b}{1-ab}
a
∗
b
=
1
−
ab
a
−
b
. What is
(
1
∗
(
2
∗
(
3
∗
⋯
(
n
∗
(
n
+
1
)
)
⋯
)
)
)
(1*(2*(3*\cdots (n*(n+1))\cdots )))
(
1
∗
(
2
∗
(
3
∗
⋯
(
n
∗
(
n
+
1
))
⋯
)))
?
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