MathDB

Let

n

be an integer,

n \geq 3.

Let

a_1, a_2, \ldots, a_n

be real numbers such that

2 \leq a_i \leq 3

for i \equal{} 1, 2, \ldots, n. If s \equal{} a_1 \plus{} a_2 \plus{} \ldots \plus{} a_n, prove that
\frac{a^2_1 \plus{} a^2_2 \minus{} a^2_3}{a_1 \plus{} a_2 \minus{} a_3} \plus{} \frac{a^2_2 \plus{} a^2_3 \minus{} a^2_4}{a_2 \plus{} a_3 \minus{} a_4} \plus{} \ldots \plus{} \frac{a^2_n \plus{} a^2_1 \minus{} a^2_2}{a_n \plus{} a_1 \minus{} a_2} \leq 2s \minus{} 2n.

Problem Statement