Find The Value Of The Floor Function

Algebra Level 5

Find $\left\lfloor \frac{33}{29}\times \frac{41}{37}\times \frac{49}{45}\times \cdots \times \frac{2009}{2005}\times \frac{2017}{2013} \right\rfloor .$

Details and assumptions

The function $\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$ refers to the greatest integer smaller than or equal to $x$ . For example $\lfloor 2.3 \rfloor = 2$ and $\lfloor -5 \rfloor = -5$ .

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