How do you use the binomial series to expand 1 / (1+x)^4?

1 Answer
Feb 1, 2016

1 - 4x +10x^2 - 20x^3 + 35x^4 +......

Explanation:

rewrite as (1+x)^-4
Since there is a negative exponent use the following version
of the binomial expansion.

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

(here n = -4 )

1 +(-4)x+((-4)(-5))/(2!) x^2+((-4)(-5)(-6))/(3!) x^3 + ...

= 1 -4x +(20)/2 x^2 -(120)/6 x^3 + ...

rArr(1+x)^-4 ≣ 1 - 4x + 10x^2 -20x^3 + 35x^4 +....