Bernoulli inequality

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.