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The binomial approximation is useful for approximately calculating powers of sums of a small number and 1. This can greatly simplify mathematical expressions see example and is a common tool in physics. This approximation can be proven several ways including the binomial theorem and ignoring the terms beyond the first two. Thus, standard linear approximation tools from calculus apply: This result from the binomial approximation can always be improved by keeping additional terms from the Taylor Series above.

While the expression is small, it is not exactly zero. It is possible to extract a nonzero approximate solution by keeping the quadratic term in the Taylor Series, i.

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