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Expansion of a term with power 2/3

  1. Aug 22, 2011 #1
    1. The problem statement, all variables and given/known data
    how am i suppose to expand

    (X-4)2/3


    3. The attempt at a solution

    i don't have any idea :(

    any help?

    thanks!
     
  2. jcsd
  3. Aug 22, 2011 #2
    oh i realise its bionomial expasion...

    i never knew the power could be a fraction :X
     
  4. Aug 22, 2011 #3

    uart

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    Science Advisor

    Yes the binomial expansion can be extended to non integer powers as :

    [tex](1 + x)^a = 1 + a x + a (a-1) \, \frac{x^2}{2!} + a (a-1)(a-2) \, \frac{x^3}{3!} + ...[/tex]

    This is an infinite series, but as you can easily see it terminates after a+1 terms (indeed to the regular binomial series) if "a" is a non-negative integer.
     
  5. Aug 22, 2011 #4
    oh i see thank you, but it doesn't terminate if a is a fraction right?
     
  6. Aug 22, 2011 #5

    uart

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    Science Advisor

    Yeah that's right, if "a" is anything other than a non-negative negative integer (that is, if its either negative or a fraction) then it's an infinite series.

    It terminates for non-negative integers because eventually one of the terms in a(a-1)(a-2) ... goes to zero.
     
  7. Aug 22, 2011 #6
    i see thank you
     
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