Taylor series strategy

  • Thread starter frasifrasi
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  • #1
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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)?
 

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  • #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?
 
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  • #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).
 
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  • #4
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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.
 
  • #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
 
  • #6
morphism
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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.
Read my post...
 
  • #7
HallsofIvy
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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.

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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