Origin of approximation

  • #1
Beer-monster
296
0
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 whats 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?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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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.
 
  • #3
Beer-monster
296
0
Thanks a lot.

Could you tell me which series that is?
 
  • #4
Dick
Science Advisor
Homework Helper
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Thanks a lot.

Could you tell me which series that is?

Geometric. The easiest of all.
 
  • #5
Beer-monster
296
0
I see it now.:blushing:

Been a while since I last saw one of those.
 

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