Core 2 help

1. Apr 16, 2007

CathyLou

Hi.

I'm completely stuck on the following question, and have no idea how to even start it.

Any help would be really appreciated.

The first four terms, in ascending powers of x, of the binomial expansion of (1 + kx)^n are

1 + Ax + Bx^2 + Bx^3 + ...,

where k is a positive constant and A,B and n are positive intgers.

(a) By considering the coefficients of x^2 and x^3, show that 3 = (n - 2)k.

Thank you.

Cathy

2. Apr 16, 2007

HallsofIvy

Staff Emeritus
Do you know the "binomial theorem":
$$(a+ b)^n= \sum_{i=0}^n _nC_i a^i b^{n-i}$$
where $_nC_i$ is the "binomial coefficient" n!/i!(n-i)!.

In particular, the coefficient if xi in (1+ kx)^n is $_nC_i k^i$
Here, you are GIVEN that the coefficient of x2, which is k2n(n-1)/2, and the coefficient of x3, which is k3n(n-1)(n-2)/6 are equal. Set them equal and cancel everything you can.

3. Apr 16, 2007

CathyLou

Okay. Thanks very much for your help!

Cathy