Inverse Squares Product

Calculus Level 3

Let

f(n)=i=1n(11(i+1)2)f(n)\quad =\quad \prod _{ i=1 }^{n }{ \left( 1-\frac { 1 }{ { \left( i+1 \right) }^{ 2 } } \right) }

Determine f(1999)f(1999).

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