Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.7 AIME Find the answer

Evaluate $\frac{2016!^{2}}{2015!2017!}$ . Here $n$ ! denotes $1 \times 2 \times \cdots \times n$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

$\frac{2016!^{2}}{2015!2017!}=\frac{2016!}{2015!} \frac{2016!}{2017!}=\frac{2016}{1} \frac{1}{2017}=\frac{2016}{2017}$

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