Binomial approximation

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The binomial approximation is useful for approximately calculating powers of numbers close to 1. It states that if x is a real number close to 0 and α is a real number, then

(1 + x)^\alpha \approx 1 + \alpha x.

This approximation can be obtained by using the binomial theorem and ignoring the terms beyond the first two.

The left-hand side of this relation is always greater than or equal to the right-hand side for x > − 1 and α a non-negative integer, by Bernoulli's inequality.