MathDB

1

Part of India EGMO 2022 TST

Problems(1)

Interesting inequality in n variables

Source: India EGMO 2022 TST P1

11/21/2021
Let n≥3n\ge 3 be an integer, and suppose x1,x2,⋯ ,xnx_1,x_2,\cdots ,x_n are positive real numbers such that x1+x2+⋯+xn=1.x_1+x_2+\cdots +x_n=1. Prove that x11−x2+x21−x3⋯+xn−11−xn+xn1−x1<2.x_1^{1-x_2}+x_2^{1-x_3}\cdots+x_{n-1}^{1-x_n}+x_n^{1-x_1}<2.
~Sutanay Bhattacharya
inequalitiesWeighted AM-GM