Edexcel P2 2021 June — Question 4

Exam BoardEdexcel
ModuleP2 (Pure Mathematics 2)
Year2021
SessionJune
TopicBinomial Theorem (positive integer n)
TypeNumerical approximation using expansion

  1. (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.