# How do you use the binomial series to expand (1 - x)^(-1/2)?

##### 1 Answer
Dec 16, 2015

$= 1 + \left(\frac{1}{2}\right) x + \left(\frac{3}{8}\right) {x}^{2} + \left(\frac{5}{16}\right) {x}^{3} + . .$

#### Explanation:

In the binomial expansion formula for (1+x)^n = 1 +nx+ (n(n-1))/(2!)x^2 + ...

substitute -x for x and $- \frac{1}{2}$ for n. The result would be

1+(-1/2)(-x) + (-1/2)(-3/2) (-x)^2 /(2!) +...

$= 1 + \left(\frac{1}{2}\right) x + \left(\frac{3}{8}\right) {x}^{2} + \left(\frac{5}{16}\right) {x}^{3} + . .$