Question

$\sum_{} \frac{1}{1 + x^{a - b} + x^{a - c}} =$

Easy

Solution

$\sum_{} \frac{1}{1 + x^{a - b} + x^{a - c}} = \sum_{} \frac{x^{b + c}}{x^{b + c} + x^{c + a} + x^{a + b}} = \frac{1}{x^{b + c} + x^{c + a} + x^{a + b}} \sum_{} x^{b + c} = \frac{1}{x^{b + c} + x^{c + a} + x^{a + b}} (x^{b + c} + x^{c + a} + x^{a + b}) = 1 .$

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