Help with expansion of an expression

[sliorbra]

Hello,

I have a problem to understand how the author made the following expansion:


1/sqrt{1+[2(r-r')*d]/(r-r')^2}≈1-{[(r-r')*d]/(r-r')^2+...}

where all the letters go for vectors and the symbol '*' is the dot product.
I suppose it is a Taylor expansion, but i just don't get it in this case.


Can someone give me the way?

 

[mfb]

1/sqrt(1+x) ≈ 1/(1+x/2) ≈ 1-x/2
Two taylor expansions up to the linear term.

 

[sliorbra]

thank you!