Question 0817

Maclaurin Series

2017 Paper 1 Question 1 Variant

Question

Using standard series from the List of Formulae (MF26), expand

\mathrm{e}^{- 5 x} \ln (1 + ax)

as far as the term in

{x^3,}

where

{a}

is a non-zero constant.

Hence find the value of ${a}$ for which there is no term in ${x^2.}$

[4]