I have a problem figuring this out

[JasonRox]

This is from Special Relativity, but it is not relevant to my question anyways.

I am trying to simplify this:

$${\Delta}t = \frac{\ell}{c} \left[ \frac{1}{1- \beta^2} - \frac{1}{\sqrt{1 - \beta^2}} \right]$$

- TO -

$${\Delta}t \approx \frac{\ell}{2c} \beta^2$$

For small x, $$(1 + x)^n \approx 1 + n x$$

NOTE: Problem SOLVED. Feel free to try this out yourself. Make $$x = -\beta^2$$, it makes it easier, or I think it does.

 

[uart]

Yep, It's called using the first two terms of the binomial expansion and it comes in very handy. :)

 

[TenaliRaman]

One has to be careful , though approximations are common [edit]in[/edit]physics ... though it really demands sometimes to think how much approximate approximations should be :P

http://mathworld.wolfram.com/BernoulliInequality.html