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# C4 - Binomial Series Question watch

1. Hi,

I'm stuck on the following question on binomial series and would really appreciate it if someone could show me how to do it:

1) In the series expansion of √(1+px+qx²) the x and x² coefficients are both equal to 1.

a) Show that p=2 and find the value of q.

b) Find the x³ term in the series expansion of √(1+px+qx²).

Thank you very much!
2. (Original post by sweet_gurl)
Hi,

I'm stuck on the following question on binomial series and would really appreciate it if someone could show me how to do it:

1) In the series expansion of √(1+px+qx²) the x and x² coefficients are both equal to 1.

a) Show that p=2 and find the value of q.

b) Find the x³ term in the series expansion of √(1+px+qx²).

Thank you very much!
let y=px+qx^2=x(p+qx)
(1+y)^1/2=1+y/2-y^2/8+y^3/16

=1+p/2x+[q/2]x^2-1/8[p^2x^2+2pqx^3+..]+x^3/16[p^3+..
=1+(p/2)x+(q/2-p^2/8)x^2+(p^3/16-pq/4)x^3
coeff of x=1
p/2=1 hence p=2

coeff of x^2=1
q/2-4/8=1
q=3

coeff of x^3 =
8/16-6/4=-1

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