Question

How do you use the binomial series to expand `f(x)=(8+x)^(1/3)` ?

Answer 1

Since

`(1+x)^{1/3}=sum_{n=0}^infty((1/3),(n))x^n`,

by replacting `x` by 7+x,

`(8+x)^{1/3}=sum_{n=0}^infty((1/3),(n))(7+x)^n`