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

Feb 1, 2016

$1 - 4 x + 10 {x}^{2} - 20 {x}^{3} + 35 {x}^{4} + \ldots \ldots$

#### Explanation:

rewrite as ${\left(1 + x\right)}^{-} 4$
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 + ...

$= 1 - 4 x + \frac{20}{2} {x}^{2} - \frac{120}{6} {x}^{3} + \ldots$

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