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Bernoulli Inequality Mathematical Induction Calculation


Calculator to prove the inequality of any given function.

x Value:
Power (r):

Result:

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.