4. 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
4. The answer is $\mathbf{( B )}$. It can be observed that for any positive real number $x$ we have $1 \star x=$ $\frac{1 \cdot x+1}{1+x}=1$; taking $x$ as the value $2 \star(3 \star(\cdots(2017 \star 2018)))$ we get that the answer to the problem is $1 \star x=1$.