MathDB

A7

Part of 2021 IMO Shortlist

Problems(1)

Weird exponent, but ok

Source: 2021 ISL A7

7/12/2022
Let n⩾1n\geqslant 1 be an integer, and let x0,x1,…,xn+1x_0,x_1,\ldots,x_{n+1} be n+2n+2 non-negative real numbers that satisfy xixi+1−xi−12⩾1x_ix_{i+1}-x_{i-1}^2\geqslant 1 for all i=1,2,…,n.i=1,2,\ldots,n. Show that x0+x1+⋯+xn+xn+1>(2n3)3/2.x_0+x_1+\cdots+x_n+x_{n+1}>\bigg(\frac{2n}{3}\bigg)^{3/2}.Pakawut Jiradilok and Wijit Yangjit, Thailand
ISL 2021algebraInequalityinequalities