MathDB

5

Part of 2006 Austrian-Polish Competition

Problems(1)

Classical

Source: APMC 2006, Problem 5

9/9/2006
Prove that for all positive integers nn and all positive reals a,b,ca,b,c the following inequality holds: an+1an+an−1b+…+bn+bn+1bn+bn−1c+…+cn+cn+1cn+cn−1a+…+an≥a+b+cn+1\frac{a^{n+1}}{a^{n}+a^{n-1}b+\ldots+b^{n}}+\frac{b^{n+1}}{b^{n}+b^{n-1}c+\ldots+c^{n}}+\frac{c^{n+1}}{c^{n}+c^{n-1}a+\ldots+a^{n}}\\ \ge \frac{a+b+c}{n+1}
inequalitiesinequalities proposed