Bernoulli Inequality

n

2

right edge of window

1

The Bernoulli Inequality states that for

x>-1

and n an integer greater than 1:

n

(1+x)

≥1+nx

with equality if and only if

x=0

. 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=0

.