Expanding Equations: Simplifying 1/(x√(1-2cosθ/x)) for Higher Order Solutions

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SUMMARY

The discussion focuses on expanding the expression 1/(x√(1-2cosθ/x)) in powers of 1/x up to the order of 1/x^3. The user is seeking guidance on whether to apply Taylor expansion for this simplification, despite not having specific values for Ao or Xo. A hint is provided regarding the expansion of 1/√(1-a) in terms of a, which is crucial for deriving the higher-order solutions.

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  • Understanding of Taylor series expansion
  • Familiarity with trigonometric functions, specifically cosine
  • Knowledge of algebraic manipulation involving square roots
  • Basic calculus concepts related to limits and series
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  • Research the Taylor series expansion for 1/√(1-a)
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  • Learn about the convergence of series expansions for different functions
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This discussion is beneficial for students and educators in mathematics, particularly those studying calculus and series expansions, as well as anyone involved in solving complex algebraic expressions.

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Homework Statement




Hello,
I'm in the middle of a question and I need to expand

1/(x√(1-2cosθ/x)) in powers 1/x up to order of 1/x^3


Homework Equations



The Attempt at a Solution




This is my attempt to the more complicated question.
To get to the final answer, I need to know how to expand the above question.
I've simplified to 1/(x√(1-2cosθ/x)).
now... do I use taylor expansion? But I'm not give Ao or Xo thus I can't have (X-Xo)

Please! Any help would be really appreciated! Thank you.
 
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Hi rockstar101! :smile:

Hint: what is the expansion of 1/√(1 -a) in terms of a? :wink:
 

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