Exercise 1. Calculate the number

$$
P=\frac{3}{2} \times \frac{4}{3} \times \cdots \times \frac{29}{28} \times \frac{30}{29}
$$

Only a numerical answer is expected here.
Solution to exercise 1 We start by calculating the first terms:

$\frac{3}{2} \times \frac{4}{3} \times \frac{5}{4}=\frac{5}{2}$ because the 4s and the 3s cancel out. We then understand what is happening: all the numbers between 2 and 30 (strictly) will cancel out, and finally we get $P=\frac{30}{2}=15$.