HMMT 2017 A7

Determine the largest real number $c$ such that for any 2017 real numbers $x_{1}, x_{2}, \ldots, x_{2017}$ , the inequality

$\sum_{i=1}^{2016} x_{i}\left(x_{i}+x_{i+1}\right) \geq c \cdot x_{2017}^{2}$

holds.

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

-\frac{1008}{2017}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.