A beautiful generalization of the Nesbitt Inequality

I want to discuss a beautiful inequality, that is a generalization of the famous Nesbitt inequality: (Romanian TST) For positive , prove that Clearly, if , then we get Nesbitt’s inequality, which states that . This is question 14 on Mildorf’s “Olympiad Inequalities”, and its solution comprises finding a factor to multiply this expression with,Continue reading “A beautiful generalization of the Nesbitt Inequality”

A proof of Muirhead’s Inequality

I’ve been reading Thomas Mildorf’s Olympiad Inequalities, and trying to prove the 12 Theorems stated at the beginning. I’m recording my proof of Muirhead’s Inequality below. Although it is probably known to people working in this area, I could not find it on the internet. Muirhead’s Inequality states the following: if the sequence majorizes theContinue reading “A proof of Muirhead’s Inequality”