# Bernoullis Inequality

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## Definition: Bernoullis Inequality

Bernoulli’s Inequality approximates the exponentiations of 1+x. the inequality states that

(1+x)^r  >=  1+rx , for x>= - 1 and r>=0 ,

this holds true for every integer r and every real number x.

Bernoulli’s inequality is a part of statistics which simplifies complex calculations and saves valuable time. This is an approximation to the accurate value which fits the consideration set every time.

If r is even, the equation (1+x) ^r > 1+rx holds true for all real numbers of x. While there is another form of Bernoulli’s Inequality such as (1+x) ^r > 1+rx which holds for r>=2 and x>=-1 except for X not equal to zero. The proof of many inequalities is based on Bernoulli’s inequality which has been proved through induction.

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