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JBMO-SL 2011 A9

Let x1,x2,…,xnx_{1}, x_{2}, \ldots, x_{n} be real numbers satisfying ∑k=1n−1min⁡(xk;xk+1)=min⁡(x1,xn)\sum_{k=1}^{n-1} \min \left(x_{k} ; x_{k+1}\right)=\min \left(x_{1}, x_{n}\right).

Prove that ∑k=2n−1xk≥0\sum_{k=2}^{n-1} x_{k} \geq 0.

Dataset text NuminaMath olympiads. Quoted with source.

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