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Homework Help: Taylor series

  1. Oct 12, 2009 #1
    I can't work out how to calculate the Taylor series for

    [tex] \frac{1}{|R-r|} [/tex]

    when R>>r, but they are both vectors. We were told to expand in r/R but I did the step below and I'm not sure where to go from there

    I got to

    [tex] \frac{1}{R \sqrt{1 - (2R.r)/R^2 + (r^2)/(R^2)}} [/tex]

    I also know the result in first order is

    [tex] \frac{1}{R} + \frac{R.r}{R^3} [/tex]
  2. jcsd
  3. Oct 12, 2009 #2


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    Gold Member

    Simplify and rewrite your expression as
    \frac{1}{R \sqrt{1 - 2r/R + (r/R)^2}}

    Now define a (small) quantity ε =r/R in terms of which you have

    \frac{1}{R \sqrt{1 - 2r/R + (r/R)^2}} =\frac{1}{R}f(\epsilon)


    Expand f(ε) in Taylor series the usual way, then replace ε with r/R.
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