MathDB

Let

n \geq 2, n \in \mathbb{N}

and let

p, a_1, a_2, \ldots, a_n, b_1, b_2, \ldots, b_n \in \mathbb{R}

satisfying

\frac{1}{2} \leq p \leq 1,

0 \leq a_i,

0 \leq b_i \leq p,

i \equal{} 1, \ldots, n, and \sum^n_{i\equal{}1} a_i \equal{} \sum^n_{i\equal{}1} b_i. Prove the inequality: \sum^n_{i\equal{}1} b_i \prod^n_{j \equal{} 1, j \neq i} a_j \leq \frac{p}{(n\minus{}1)^{n\minus{}1}}.

Problem Statement