Answer to Question #319946 in Calculus for atharva23

Question

expand (1+x)^-2 using binomial theorem

Answer 1

Binomial theorem

$(1+x)^{n}=1+nx+\frac{n(n-1)}{2!}x^2+...$

Here $n=-2$

$(1+x)^{-2}=1-2x+\frac{-2(-2-1)}{2!}x^2+...$

$=1-2x+\frac{6}{2!}x^2+...$

$=1-2x+\frac{6}{2}x^2+...$

$=1-2x+3x^2+....$