How is this approximation derived?

Question

What is the argument behind: 1/(1+x) can be approximated by 1-x if x<<1 ?

I couldn't find where this approximation comes from/derived.

Answer 1

It's because near $0$ we have\begin{align}\frac1{1+x}&=1-x+x^2-x^3+\cdots\text{ (it's the sum of a geometric series)}\\&\simeq1-x.\end{align}