Can anyone help me with this C4 binomial expansion question, please?

Given that 1 = (1 +x + x^2)(A + Bx + Cx^2 + Dx^3 + Ex^4+...) equate coefficients of power of x to find values A,B,C,D,E.

I worked out A = 1 B = -1 C = 0 D = 1 E = -1

(a) Find the value of 1/1.00030009 correct to 16 decimal places;

(b)Show that 1/((1+ x + x^2)(1+ 2x+ 4x^2)) ≈ 1 - 3x+ 2x^2 + 9x^3 + 27x^4) for small values of x

I don't understand how to do part (a) or (b)

Can anyone help me please? I'm stuck.

Reply 1

JN17

For (a) compare what you're given to the first bit, so 1/(1+x+x^2) = A+Bx..., how could you make 1+x+x^2 equal to 1.00030009? Use that value of x with the A+Bx.. part for an answer.
For (b) you are multiplying your A+Bx... part by 1/(1+2x+4x^2), so see how that works out and it should lead to the given answer.

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