- The first four terms, in ascending powers of \(x\), of the binomial expansion of \(( 1 + k x ) ^ { n }\) are
$$1 + A x + B x ^ { 2 } + B x ^ { 3 } + \ldots$$
where \(k\) is a positive constant and \(A\), \(B\) and \(n\) are positive integers.
- By considering the coefficients of \(x ^ { 2 }\) and \(x ^ { 3 }\), show that \(3 = ( n - 2 ) k\).
Given that \(A = 4\),
- find the value of \(n\) and the value of \(k\).