Question #319946

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


1
Expert's answer
2022-03-29T17:28:32-0400

Binomial theorem

(1+x)n=1+nx+n(n1)2!x2+...(1+x)^{n}=1+nx+\frac{n(n-1)}{2!}x^2+...

Here n=2n=-2

(1+x)2=12x+2(21)2!x2+...(1+x)^{-2}=1-2x+\frac{-2(-2-1)}{2!}x^2+...

=12x+62!x2+...=1-2x+\frac{6}{2!}x^2+...

=12x+62x2+...=1-2x+\frac{6}{2}x^2+...

=12x+3x2+....=1-2x+3x^2+....


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