# Least value

Algebra Level 4

$$x_{1} , x_{2} , ...................................... ,x_{n}$$ are positive numbers such that

$$x_{1} + x_{2} + ...................................... + x_{n} = \frac{1}{2}$$

then the least value of

$$\displaystyle \prod_{i=1}^{i} \frac{1 - x_{i}}{1 + x_{i}} = \frac{a}{b}$$

a + b =

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