ÖMO 1991 Problem 5

For all positive integers $n$ prove the inequality:

$\left( \frac{1+(n+1)^{n+1}}{n+2} \right)^{n-1}>\left( \frac{1+n^n}{n+1} \right)^n.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.