Home Competitions ISL 2016 A8
Determine the largest real number a a a n ⩾ 1 n \geqslant 1 n ⩾ 1 x 0 , x 1 , … , x n x_{0}, x_{1}, \ldots, x_{n} x 0 , x 1 , … , x n 0 = x 0 < x 1 < x 2 < ⋯ < x n 0=x_{0}<x_{1}<x_{2}<\cdots<x_{n} 0 = x 0 < x 1 < x 2 < ⋯ < x n 1 x 1 − x 0 + 1 x 2 − x 1 + ⋯ + 1 x n − x n − 1 ⩾ a ( 2 x 1 + 3 x 2 + ⋯ + n + 1 x n ) . \frac{1}{x_{1}-x_{0}}+\frac{1}{x_{2}-x_{1}}+\cdots+\frac{1}{x_{n}-x_{n-1}} \geqslant a\left(\frac{2}{x_{1}}+\frac{3}{x_{2}}+\cdots+\frac{n+1}{x_{n}}\right) . x 1 − x 0 1 + x 2 − x 1 1 + ⋯ + x n − x n − 1 1 ⩾ a ( x 1 2 + x 2 3 + ⋯ + x n n + 1 ) .
Dataset text NuminaMath olympiads . Quoted with source.
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