Bernoulli's inequality
In mathematics, Bernoulli's inequality (named after Jacob Bernoulli) is an inequality that approximates exponentiations of 1 + x. It is often employed in real analysis. It has several useful variants: * for every integer r ≥ 0 and real number x > −1. The inequality is strict if x ≠ 0 and r ≥ 2. * for every even integer r ≥ 0 and every real number x. * for every integer r ≥ 0 and every real number x ≥ −2. * for every real number r ≥ 1 and x ≥ −1. The inequalities are strict if x ≠ 0 and r ≠ 0, 1. * for every real number 0 ≤ r ≤ 1 and x ≥ −1. (Wikipedia).
