Bernoulli's inequality in
real analysis states that
- (1 + x)n ≥ 1 + nx
for every
integer n ≥ 0 and every
real number x ≥ -1. The strict version of the inequality reads
- (1 + x)n > 1 + nx
for every integer
n ≥ 2 and every real number
x ≥ -1 with
x ≠ 0.
The inequality is often used as the crucial step in the proof of other inequalities. It can be proven using mathematical induction.