Binomial approximation

The binomial approximation is useful for approximately calculating powers of numbers close to 1. It states that if Failed to parse (Missing texvc executable; please see math/README to configure.): x

is a real number close to 0 and Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha
is a real number, then 

Failed to parse (Missing texvc executable; please see math/README to configure.): (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 Failed to parse (Missing texvc executable; please see math/README to configure.): x>-1

and Failed to parse (Missing texvc executable; please see math/README to configure.): \alpha
a non-negative integer, by Bernoulli's inequality.