Math Is Fun Forum

Tredici

Member

Registered: 2005-12-12

Posts: 28

Binomial Expansion Problem

This one looks as though it'd be easy to me, but when I get stuck in, I end up with silly simultaneous equations, which I can't seem to work with. Any help with this would be really appreciated. Thanks again lads, Tred.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Binomial Expansion Problem

for x and x^2

the coeffecients in the expansion will be

and

the bracket thingy being the binomial expansion thingy

so the ceoffecients are

...

...

...

however... (-2)! is undefined... so i dont see how that can be right

Last edited by luca-deltodesco (2006-06-12 03:29:02)

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gnitsuk

Member

Registered: 2006-02-09

Posts: 121

Re: Binomial Expansion Problem

Binomial Expansion is:

(1 + x) ^ n = 1 + n x + n (n - 1) x^2 / 2 + n (n - 1) (n - 2) x^3 / 6 + ...

Here we must substitue x with ax so we have:

a)

na = -6 => a = -6/n

n(n-1)a^2/2 = 27 => 36n(n-1)/n^2 = 54 => 36(n-1) = 54n =>

35n - 36 - 54n = 0 => -18n = 36 => n = -2

Therefore a = -6/-2 = 3

b)

Coefficient of x^3 = n(n-1)(n-2)a^3 / 6 = -2*-3*-4*a^3 / 6 = -4*a^3 = -4 * 9 = -36

c)

General Binomial is valid when |x| < 1 so here we need |3x| < 1 => |x| < 1/3

Last edited by gnitsuk (2006-06-12 20:09:28)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Binomial Expansion Problem

stuff

well ive only learnt binomial expansion with the pascal triangle stuff, but atleast it seems i did get the values of n and a correct

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