What is the Origin of the Approximation?

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Homework Help Overview

The discussion revolves around understanding an approximation found in a textbook derivation. The original poster is seeking clarity on the origin and reasoning behind the approximation, specifically related to a mathematical expression involving a series expansion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the approximation's derivation, with one suggesting the use of a series expansion and another inquiring about the specific series being referenced.

Discussion Status

Participants are engaged in clarifying the nature of the series involved in the approximation. There is an acknowledgment of the geometric series, indicating a productive direction in the discussion.

Contextual Notes

The original poster expresses difficulty in understanding the approximation due to a lack of guidance in the textbook, highlighting the challenge of deriving it independently.

Beer-monster
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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:

[tex]\frac{1}{a}\left(1-\frac{x}{a}\right)^{-1} \cong \frac{1}{a}\left(1+\frac{x}{a}\right)[/tex]


Could anyone please explain this to me?
 
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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.
 
Thanks a lot.

Could you tell me which series that is?
 
Beer-monster said:
Thanks a lot.

Could you tell me which series that is?

Geometric. The easiest of all.
 
I see it now.:blushing:

Been a while since I last saw one of those.
 

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