Maximizing Reciprocals

Algebra Level 4

Let x1,x2,,xnx_1, x_2, \dots, x_n be positive reals satisfying x1x2xn=1x_1x_2 \cdots x_n = 1.

Find the maximum value of 1n1+x1+1n1+x2++1n1+xn. \dfrac{1}{n-1+x_1} + \dfrac{1}{n-1+x_2} + \dots + \dfrac{1}{n-1+x_n} .

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