Bernoulli Inequality Calculator

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

When n≥1, \((1+x)^n≥1+nx\) is established;

When 0 ≤ n ≤ 1, \((1+x)^n ≤ 1+nx\) holds.

You can see that the equal sign is true 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, both have xi >= -1 and sign(xi) = sign(xj), ie all xis with the same number and greater than or equal to -1) if and only if When n=1, the equal sign is established.

Note: The letter or number after x is the subscript

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