# Maximizing Reciprocals

Algebra Level 4

Let $x_1, x_2, \dots, x_n$ be positive reals satisfying $x_1x_2 \cdots x_n = 1$.

Find the maximum value of $\dfrac{1}{n-1+x_1} + \dfrac{1}{n-1+x_2} + \dots + \dfrac{1}{n-1+x_n} .$

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