bernoulli's inequality in mathematics says: for real numbers x>-1,

when n≥1, there is (1+x)ⁿ≥1+nx is established;

when 0≤n≤1, there is (1+x)ⁿ≤1+nx is established.

you can see that the equal sign 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, has xi >= -1 and sign(xi) = sign(xj), that is, all xi have the same sign and are greater than or equal to -1) equal sign if and only if n=1 established

note: the letters or numbers after x are subscripts