Wednesday, October 3, 2018

Yet another inequality

$x_1, x_2, \dots, x_n$ are $n$ positive real numbers with sum $S$, $n \gt 1$.

Show that

$$ \sum_{i=1}^{n} \frac{x_i}{S - x_i} \ge \frac{n}{n-1}$$


Solution [Click here to expand/collapse]

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