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Math Help - Binomial Theorum questions!

  1. #1
    LHS
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    Exclamation Binomial Theorum questions!



    A bit stuck on 5 and the second half of 6, I keep getting 1/4 for the coefficent of x^2 in 5. Thanks
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  2. #2
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    sqrt.[(1+x)/(1-x)]=(1+x)/sqrt.(1-x^2)=(1+x)*(1-x^2)^-(1/2)

    =(1+x)*[1-(-1/2)*x^2]

    =(1+x)*[1+x^2/2]

    =1+x+x^2/2+x^3/2.

    question 2>take x=0.01,u get,97^(3/2)/1000.
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  3. #3
    LHS
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    Are you sure on that first part? Check your sqrt'ing of the top bracket
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  4. #4
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    I AM 100% SURE.

    i dont know if u have read it clearly.

    (1+x)*[(1-x^2)^-(1/2)]=(1+x)*[1-(-1/2)x^2]
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  5. #5
    LHS
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    How is that helping prove that the approx expansion is: 1+x+(1\2)x^2?
    I had sqrt((1+x)/(1-x)) = ((1+x)^(1/2))*((1-x)^(-1/2))
    I expanded those up to x^1 and got (1+(1/2)x)*(1+(1/2)x) using the binomial theorem, then that expands to 1+x+(1/4)x^2, very close to the answer, wondering if the book got it wrong..
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  6. #6
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    but u could see,that i've already proved it in my first post,friend.

    the book is not wrong,
    the solution process varies.
    i think my solution is the right one.
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  7. #7
    LHS
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    Ok, well thank you for your help!
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