Binomial expansion help

• June 2nd 2009, 07:15 AM
iamnoob
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
• June 3rd 2009, 03:52 AM
CaptainBlack
Quote:

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:

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

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

CB
• June 3rd 2009, 06:35 AM
iamnoob
thanks alot captain black =D