(Special relativity) Binomial Approximation

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Homework Help Overview

The discussion revolves around the application of the binomial approximation in the context of special relativity, specifically focusing on the Lorentz factor (γ) and its related expressions. Participants are exploring how to derive specific equations involving γ and the variable β, which represents velocity as a fraction of the speed of light.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to derive expressions for γ and its reciprocal using the binomial approximation. There are questions about the arithmetic involved in deriving one expression from another, as well as inquiries into the expansion of functions related to the binomial theorem.

Discussion Status

The discussion is active, with participants offering various approaches to derive the requested expressions. Some guidance has been provided regarding arithmetic and function expansion, but there is no explicit consensus on the methods being discussed.

Contextual Notes

Participants are considering the implications of using the binomial approximation and questioning the appropriateness of applying it to different forms of the equations. There is an acknowledgment of the complexity involved in deriving the expressions without complete clarity on all steps.

ak345
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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)
 
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For C, from B, arithmetic.
 
For B from A, what is expansion of 1/(1+x) ?
 

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