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.