Bernoulli's inequality

In mathematics, Bernoulli's inequality (named after Jacob Bernoulli) is an inequality that approximates exponentiations of . It is often employed in real analysis. It has several useful variants: Integer exponent Case 1: for every integer and real number . The inequality is strict if and . Case 2: for every integer and every real number . Case 3: for every even integer and every real number . Real exponent for every real number and . The inequality is strict if and . for every real number and . History Jacob Bernoulli first published the inequality in his treatise "Positiones Arithmeticae de Seriebus Infinitis" (Basel, 1689), where he used the inequality often.