In math, Bernoulli inequality (math.) says: for the real number x>-1,

When n≥1, (1+x)ⁿ≥1+nx is established;

When 0≤n≤1, (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 inequality (math.) is often used as a key step in proving other inequalities (math.).

Bernoulli inequality (math.) The general formula is (1+x1+x2+x3···+xn)< =(1+x1)(1+x2)(1+x3)···(1+xn), (For arbitrarily 1 <= i,j <= n, xi >= -1 and sign(xi) = sign(xj), that is, all xi are the same sign and greater than be tantamount to -1) The equality sign is valid if and only if n=1

Note: letter or Number after x is subscript