Find the first four terms in the expansion of (1 − x)− 12

The expansion of (1 - x)^(-1/2) can be found using the binomial theorem for negative and fractional powers. The binomial theorem states that:

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

For n = -1/2, the first four terms of the expansion are:

1 - (1/2)x + (1/2)(-3/2)x^2/2! - (1/2)(-3/2)(-5/2)x^3/3!

Simplifying these terms gives:

1 - (1/2)x + 3/8x^2 - 15/48x^3

So, the first four terms in the expansion of (1 - x)^(-1/2) are 1, -(1/2)x, 3/8x^2, and -15/48x^3.