1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    3. The attempt at a solution

    i don't have any idea :(

    any help?

  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


    User Avatar
    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


    User Avatar
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook