I would like some confirmation that I have done the following binomial expansion to two terms correctly, here is what I have got:
I have to approximate $\frac{1}{\sqrt{r^2+a^2-2racos\theta}}$ for $r>>a$
I transformed it into this: $\frac{1}{r}(\frac{a^2-2arcos\theta}{r^2})^{-\frac{1}{2}}$
Then using the formula $(1+x)^\alpha=1+\alpha x...$
I get this: $\frac{1}{r}(1-\frac{a^2-2arcos\theta}{2r^2})$
Is this correct or where have I gone wrong?