What is the Origin of the Approximation?

[Beer-monster]

Hi

Homework Statement

I'm trying to follow and work through a derivation in my textbook, making sure I can replicate the steps myself and understand what's happening. However, I came across this approximation and can't seem to figure out where it comes from or why and the book gives no clues.

Homework Equations

The general form is:

$$\frac{1}{a}\left(1-\frac{x}{a}\right)^{-1} \cong \frac{1}{a}\left(1+\frac{x}{a}\right)$$


Could anyone please explain this to me?

 

[Dick]

1/(1-y)=1+y+y^2+y^3+... The series converges if y<1. Put y=(x/a) and approximate by only keeping the first two terms.

 

[Beer-monster]

Thanks a lot.

Could you tell me which series that is?

 

[Dick]

Thanks a lot.

Could you tell me which series that is?

Geometric. The easiest of all.

 

[Beer-monster]

I see it now.

Been a while since I last saw one of those.