Question 67
Given two positive real numbers $a, b$ we define
$$
a \star b=\frac{a b+1}{a+b}
$$
What is the value of $1 \star(2 \star(3 \star(\cdots(2017 \star 2018))))$?
(A) $1 / 2018$
(B) 1
(C) $2018 / 2017$
(D) 1009
(E) 2018
$$
a \star b=\frac{a b+1}{a+b}
$$
What is the value of $1 \star(2 \star(3 \star(\cdots(2017 \star 2018))))$?
(A) $1 / 2018$
(B) 1
(C) $2018 / 2017$
(D) 1009
(E) 2018