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Problem of the week

For an integer \( n \geq 3 \), evaluate \[ \inf \left\{ \sum_{i=1}^n \frac{x_i^2}{(1-x_i)^2} \right\}, \] where the infimum is taken over all \( n \)-tuple of real numbers \( x_1, x_2, \dots, x_n \neq 1 \) satisfying that \( x_1 x_2 \dots x_n = 1 \).