- The binomial expansion of
$$( 1 + a x ) ^ { 12 }$$
up to and including the term in \(x ^ { 2 }\) is
$$1 - \frac { 15 } { 2 } x + k x ^ { 2 }$$
where \(a\) and \(k\) are constants.
- Show that \(a = - \frac { 5 } { 8 }\)
- Hence find the value of \(k\)
Using the expansion and making your method clear,
- find an estimate for the value of \(\left( \frac { 17 } { 16 } \right) ^ { 12 }\), giving your answer to 4 decimal places.