Question

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

Answer 1

`=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 +..`