Question

How do you use the binomial series to expand `f(x)=1/(1+x)^3`?

Answer 1

the answer is `f(x)=1-3x+6x^2-10x^3+15x^4+.....`

Explanation:

The binomial expansion is `(a+b)^n`
`=a^n+na^(n-1)b+(n(n-1))/(1*2)a^(n-2)b^2+.......`

Applying this here with `a=1`, `b=x` and `n=-3`
we get
`f(x)=(1+x)^-3=1-3x+((-3)(-4))/(1*2)x^2+((-3)(-4)(-5))/(1*2*3)x^3+((-3)(-4)(-5)(-6))/(1*2*3*4)x^4+......`
`=1-3x+6x^2-10x^3+15x^4+.....`