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sums with minimums in R

Source: JBMO 2011 Shortlist A9

October 14, 2017
JBMOalgebra

Problem Statement

Let x1,x2,...,xnx_1,x_2, ..., x_n be real numbers satisfying ∑k=1n−1min(xk;xk+1)=min(x1;xn)\sum_{k=1}^{n-1} min(x_k; x_{k+1}) = min(x_1; x_n). Prove that ∑k=2n−1xk≥0\sum_{k=2}^{n-1} x_k \ge 0.
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