HMMT 2005 U6

Let $m \circ n=(m+n) /(m n+4)$ . Compute $((\cdots((2005 \circ 2004) \circ 2003) \circ \cdots \circ 1) \circ 0)$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1}{12}

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