Question 0810

Maclaurin Series

2010 Paper 1 Question 2 Variant

Question

(i)

Find the first three terms of the Maclaurin series for

\mathrm{e}^{2 x} (1 + \sin 3 x).

[Your may use standard results given in the List of Formulae (MF26).]

[3]

(ii)

It is given that the first two terms of this series are equal to the first two terms in the series expansion, in ascending powers of

{x,}

{(1 + \frac{9}{5} x)^n.}

Find

{n}

and show that the third terms in each of these series are equal.

[3]