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Math Help - Binomial expansion help

  1. #1
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    Binomial expansion help

    hi.i've just come across this question and got stuck at part (iii).i could really use some help as i have to submit this assignment.heres the question:

    (i)Expand ((1-x)/(1+x))^n in ascending powers of x up to and including the term x^3.

    (ii) State the values of x for which the series expansion is valid.

    (iii)Hence find an approximation to the fourth root of 19/21, in the form p/q ,where p and q are positive integers.



    Ans: (i)1−2nx+2n2x2 (ii)x <1 (iii) 3121/3200
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  2. #2
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    Quote Originally Posted by iamnoob View Post
    hi.i've just come across this question and got stuck at part (iii).i could really use some help as i have to submit this assignment.heres the question:

    (i)Expand ((1-x)/(1+x))^n in ascending powers of x up to and including the term x^3.

    (ii) State the values of x for which the series expansion is valid.

    (iii)Hence find an approximation to the fourth root of 19/21, in the form p/q ,where p and q are positive integers.



    Ans: (i)1−2nx+2n2x2 (ii)x <1 (iii) 3121/3200
    For part (iii) observe that:

    \frac{19}{20}=\frac{20-1}{20+1}=\frac{1-\frac{1}{20}}{1+\frac{1}{20}}

    So now use your approximation with x=\frac{1}{20} and n=\frac{1}{4} to get the required rational approximation.

    CB
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  3. #3
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    thanks alot captain black =D
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