Bernoulli Inequality Calculator

The Bernoulli inequality in mathematics says: for real numbers x>-1,

when n≥1, (1+x)ⁿ≥1+nx holds;

when 0≤n≤1, (1+x)ⁿ≤1+nx holds.

You can see that the equality holds if and only if n = 0,1, or x = 0. Bernoulli's inequality is often used as a key step in proving other inequalities.

The general formula of Bernoulli's inequality is (1+x1+x2+x3···+xn)< =(1+x1)(1+x2)(1+x3)···(1+xn), (for any 1 <= i,j <= n, there is xi >= -1 and sign(xi) = sign(xj), that is, all xi have the same sign and are greater than or equal to -1) The equality is established when and only when n=1

Note: The letters or numbers after x are subscripts