# Bernoulli Inequality Mathematical Induction Calculation

Calculator to prove the inequality of any given function.

Bernoulli’s Inequality is defined as an inequality that approximates exponentiations of 1 + x.

where the inequality states that for every integer r ≥ 0 and every real number x ≥ −1.

In the case of exponent r is even, then the inequality is valid for all real numbers x.

The Bernoulli inequality states (1 + x)^{r} ≥ 1 + rx.

Where,

x ≥ -1 and x ≠ 0,

r ≥ 1

## Example

**Prove the inequality of any given function where x = 8 and r = 2.**

The Bernoulli inequality states (1 + x)^{r} ≥ 1 + rx.

That is, (1 + 8)^{2} ≥ 1 + 2 x 8.

≡ (9)^{2} ≥ 1 + 16.

≡ 81 > 17.