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Problem 697

AIME late

Algebra Difficulty 5.2 Find the answer

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.

Your answer

Official solution

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 $P=\frac{30}{2}=15$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.