Binomial Theorem/Approximations

Theorem
Consider the General Binomial Theorem:
 * $\paren {1 + x}^\alpha = 1 + \alpha x + \dfrac {\alpha \paren {\alpha - 1} } {2!} x^2 + \dfrac {\alpha \paren {\alpha - 1} \paren {\alpha - 2} } {3!} x^3 + \cdots$

When $x$ is small it is often possible to neglect terms in $x$ higher than a certain power of $x$, and use what is left as an approximation to $\paren {1 + x}^\alpha$.