15. The binomial expansion, in ascending powers of \(x\), of \(( 1 + k x ) ^ { n }\) is
$$1 + 36 x + 126 k x ^ { 2 } + \ldots$$
where \(k\) is a non-zero constant and \(n\) is a positive integer.
- Show that \(n k ( n - 1 ) = 252\)
- Find the value of \(k\) and the value of \(n\).
- Using the values of \(k\) and \(n\), find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(( 1 + k x ) ^ { n }\)