1. ## Binomial expansion

Hi guys!

I have a homework question about the binomial expansion:

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 integers.

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

Any help would be really great

2. $\left( {1 + kx} \right)^n = \sum\limits_{j = 0}^n {\binom{n}{j}\left({kx} \right)^j } = 1 + nkx + \frac{{n\left( {n - 1} \right)}}
{{2!}}k^2 x^2 + \frac{{n(n - 1)(n - 2)}}
{{3!}}k^3 x^3 + \cdots$

3. I have that part, but i'm not sure how it simplifies down to give 3=(n-2)k
(this is probably a stupid question...)

4. $\begin{gathered}
B = B \hfill \\
\frac{{n\left( {n - 1} \right)}}
{{2!}}k^2 = \frac{{n(n - 1)(n - 2)}}
{{3!}}k^3 \hfill \\
3 = \left( {n - 2} \right)k \hfill \\
\end{gathered}$