SE-SKOLORNAS 1972 Problem 5

Show that $\int\limits_0^1 \frac{1}{(1+x)^n} dx > 1-\frac{1}{n}$ for all positive integers $n$ .

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.