Question 103
For positive real numbers $x, y$, the positive real number $x \star y$ is defined as $x \star y = \frac{x}{xy+1}$.
Calculate the following expression:
$$
(((\cdots (((100 \star 99) \star 98) \star 97) \star \cdots) \star 3) \star 2) \star 1.
$$
Calculate the following expression:
$$
(((\cdots (((100 \star 99) \star 98) \star 97) \star \cdots) \star 3) \star 2) \star 1.
$$