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Where does this approximation come from?

  1. Apr 11, 2013 #1
    [tex]\frac{\sqrt{1-a}}{\sqrt{1-b}}\approx \left ( 1-\frac{1}{2}a\right )\left ( 1+\frac{1}{2}b\right )[/tex]

    I know that the binomial approximation is first used,

    [tex]\frac{\sqrt{1-a}}{\sqrt{1-b}}\approx \frac{1-\frac{1}{2}a}{1-\frac{1}{2}b}[/tex]

    But how does one approximate:

    [tex]\frac{1-\frac{1}{2}a}{1-\frac{1}{2}b}\approx \left ( 1-\frac{1}{2}a\right )\left ( 1+\frac{1}{2}b\right )[/tex]?
  2. jcsd
  3. Apr 11, 2013 #2
    Do you know the series for [itex]\frac{1}{1-x}[/itex] ?
  4. Apr 11, 2013 #3
    No, unfortunately. Is there a name for this approximation?
  5. Apr 11, 2013 #4


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    The expression can be rearranged to: ##\displaystyle {(1-a)}^{\frac{1}{2}}{(1-b)}^{-\frac{1}{2}}##. Now apply the binomial approximation to each term.
  6. Apr 11, 2013 #5
    Ahh, I see. Thanks!
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