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

1 Answer
Dec 16, 2015

=1+ (1/2)x +(3/8)x^2 + (5/16) 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 -1/2 for n. The result would be

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

=1+ (1/2)x +(3/8)x^2 + (5/16) x^3 +..