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Binomial Expansion

  1. Aug 26, 2009 #1
    Hi, its me again.

    [tex]\left(1 - x\right)^{\frac{1}{5}}[/tex]

    show that [tex]31.2^{\frac{1}{5}} \approx \frac{197}{99} [/tex]


    how can i know what value should x be ?
     
  2. jcsd
  3. Aug 26, 2009 #2
    In order for the binomial expansion to hold, the absolute value of x must be less than 1. In this case, since we are going to approximate it as a fraction, we would want to end up with nice simplifiable roots. This would point us towards 2^5, 32. From there, you can get x after manipulation.
     
  4. Aug 27, 2009 #3
    Still don't get it. so i let 1 - x = 32 ?

    or i extract 32 out so 31.2/32 =0.975
    and then let it be

    [32(0.975)]^1/5
    (2)(1-0.025)^1/5

    then let x = 0.025?
     
  5. Aug 27, 2009 #4
    Try Maclaurin series (=
     
  6. Aug 27, 2009 #5
    Yup, thats the way to do it.
    Bleh, I hate Maclaurin's lol, never use it unless necessitated.
     
  7. Aug 27, 2009 #6

    Mark44

    Staff: Mentor

    There is a forum for calculus problems. This one is for precalculus problems.
     
  8. Aug 27, 2009 #7
    I'm sorry, actually i can't differentiate which is calculus and which is not ._. In my country its just Maths S and Maths T i don't even know what it stands for. I never heard of Maclaurin series O-o
     
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