(Special relativity) Binomial Approximation

[ak345]

Use the binomial approximation to derive the following:
A) γ=1+.5(β^2)
B)1/γ=1-.5(β^2)
C)1-(1/γ)=.5(^2)

I know the approximation is 1+(.5β^2)+(3/8)β^4+...
A) is self explanatory but not sure how to derive B) and C)

 

[PAllen]

For C, from B, arithmetic.

 

[PAllen]

For B from A, what is expansion of 1/(1+x) ?

 

[ChrisVer]

$\gamma = ( 1 - \beta^{2}) ^ {-\frac{1}{2}} = \frac{1}{ \sqrt{1+x}}, ~~ x= - \beta^{2}$
Why not use the binomial for the:
$\gamma^{-1}$?
http://en.wikipedia.org/wiki/Binomial_theorem