# Bernoulli Inequality

Bernoulli Inequality

The Bernoulli Inequality states that for and n an integer greater than 1: ≥1+nx with equality if and only if . This Demonstration shows, for various integer values of n greater than 1, the graph of the left-hand side of the inequality in blue and the graph of the right-hand side in red. Use the sliders to adjust the value of n and the viewing window and notice that the blue curve is always above the red one, with the only contact occurring at .

x>-1

n

(1+x)

x=0

x=0