- (a) Find, in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\), the binomial expansion of
$$\left( 2 + \frac { x } { 8 } \right) ^ { 13 }$$
fully simplifying each coefficient.
(b) Use the answer to part (a) to find an approximation for \(2.0125 ^ { 13 }\)
Give your answer to 3 decimal places.
Without calculating \(2.0125 { } ^ { 13 }\)
(c) state, with a reason, whether the answer to part (b) is an overestimate or an underestimate.