Thread: 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

Originally Posted by iamnoob

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:



So now use your approximation with and to get the required rational approximation.

CB

thanks alot captain black =D