# Least value

Algebra Level 4

$$x_1, x_2, \ldots, x_n$$ are positive numbers that sum to $$\frac{1}{2}$$. The minimum value of

$\prod_{i=1}^n \frac{ 1 - x_i } { 1 + x_i }$

can be expressed as $$\frac{a}{b}$$ for positive coprime integers $$a$$ and $$b$$. What is the value of $$a+b$$?

×