Time dilation by special relativity When reading about special relativity and time dilation I encounter a problem;
Here is a link: Time dilation in GPS 
On page 1 under header "2. Time dilation by special relativity." It says: Since $(1 – x)^{-1/2} ≈ 1 + x /2$ for small $x$, we get...
How is $(1 – x)^{-1/2} ≈ 1 + x /2$ for small $x$? I really don't get it.
Thank you in advance!

That is a mathematical approximation that is valid when $x\ll 1$ (meaning $x$ much less than one). It can be easily demonstrated if you know calculus: for any function $f(x)$ that is defined and derivable at $x=0$, $f(x)=f(0)+f'(0)x+\ldots$ (it is called a Taylor series expansion). The first two terms are enough if $x$ is small, otherwise the approximation requires more terms to be good.
