[Math] Expansion of $(a+b)^{1/3}$ with binomial theorem

Question

I want to expand $(a+b)^{1/3}$ using the binomial theorem.

1) Is it possible to do that? If not, which expansion should I look up to do so?

2) If yes, how do I evaluate $\dbinom{n}{\frac{1}{3}}$?

Thanks 🙂

Answer 1

Binomial theorem works for non negative integer $n$.

What we can do is use the binomial series expansion for

$$(a+b)^{\frac13}=a^\frac13(1+b/a)^\frac13=a^\frac13\left(1+\frac{b}{3a}-\frac{b^2}{9a^2}+...\right)$$