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# help on binomial expansion needed watch

1. (1+x)^-1
(1-3x)^½
a)use on of these expansions with a suitable value of x, to estimate the value of 1/1.001 correct to 6sf

b) use both your answers from the above binomail expansions find the first 4 terms in the series expansion of √(1-3x)/(1+x), stating the set if values of x for which the expansion is valid
2. (Original post by lil_kk)
(1+x)^-1
(1-3x)^½
a)use on of these expansions with a suitable value of x, to estimate the value of 1/1.001 correct to 6sf
let x = 0.001 in the expansion (1+x)-1 as far as x² this should give you 5 d.p or 6 sig fig accuracy...

1 + -1(x) + -1*-2(x)²/2! + ....
3. (Original post by lil_kk)
find the first 4 terms in the series expansion of √(1-3x)/(1+x), stating the set if values of x for which the expansion is valid
{1 + ½(-3x) + ½*-½(-3x)²/2! + ½*-½*-1.5(-3x)³/3!+ ...}{ 1 + -1(x) + -1*-2(x)²/2! + -1*-2*-3(x)³/3! + ...}

now simplify inside the brackets. when you have simplified you multiply out the brackets, discarding any terms involving powers of x greater than 3.

the first expansion is valid for -1<3x<1 or -1/3 < x < 1/3
the second expansion is valid for -1< x < 1

the combined expansion is valid for the more restrictive of the two ranges ie
-1/3 < x < 1/3
4. (Original post by the bear)
{1 + ½(-3x) + ½*-½(-3x)²/2! + ½*-½*-1.5(-3x)³/3!+ ...}{ 1 + -1(x) + -1*-2(x)²/2! + -1*-2*-3(x)³/3! + ...}

now simplify inside the brackets. when you have simplified you multiply out the brackets, discarding any terms involving powers of x greater than 3.

the first expansion is valid for -1<3x<1 or -1/3 < x < 1/3
the second expansion is valid for -1< x < 1

the combined expansion is valid for the more restrictive of the two ranges ie
-1/3 < x < 1/3

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Updated: November 24, 2005
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