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Taylor series strategy

  1. Dec 13, 2007 #1
    I am trying to find the maclaurin series for f(x) = (1 + x)^(-3)

    --> what is the best way of doing this--to make a table and look for a trend in f^(n)?
     
  2. jcsd
  3. Dec 13, 2007 #2

    rock.freak667

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    .....well you can do that but you will just find that is just a binomial series.


    do you know the nth term in a binomial expansion?
     
    Last edited: Dec 13, 2007
  4. Dec 13, 2007 #3

    morphism

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    Presumably you know the expansion of 1/(1+x) (hint: think geometric series). So what's the second derivative of 1/(1+x), and how does this help? This should give you another way of finding the expansion of (1+x)^(-3).
     
    Last edited: Dec 13, 2007
  5. Dec 13, 2007 #4
    NO!!! NO!! NO!! there should be no binomals involved. Is there a simpler way? the way we usually do this is by making a table.

    If someone can shed some light, I would appreciate it.
     
  6. Dec 13, 2007 #5

    rock.freak667

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    Well you will have to find f(0),f'(0),f'''(0) and so forth for the traditional method for finding the maclaurin series for that function. But I believe that you should make the table and then make the series if that is the way you know how to do it
     
  7. Dec 13, 2007 #6

    morphism

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    Read my post...
     
  8. Dec 14, 2007 #7

    HallsofIvy

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    You can, in fact, extend the binomial theorem to fractional or negative exponents. Morphism suggested an even easier way. You'[ve already been given two very good ways of finding the series. Why don't you appreciate them?
     
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