SE-SKOLORNAS 1974 Problem 2

Show that $1 - \frac{1}{k} \leq n\left(\sqrt[n]{k}-1\right) \leq k - 1$ for all positive integers $n$ and positive reals $k$ .

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.