2015 RI Promo Q8
(a)
(i) Expand $\text{f}\left( x \right)=\frac{2}{2-x}-\frac{1}{{{\left( 1+x \right)}^{2}}}$ as a series in ascending powers of $x$ up to and including the term in ${{x}^{2}}$.
[3]
(ii) State the equation of the tangent to the curve $y=\text{f}\left( x \right)$ at the origin.
[1]
(b)
Using the standard series given in the List of Formulae (MF15) or otherwise, show that the first three non- zero terms in the Maclaurin series for ${{\text{e}}^{\sqrt{1+x}}}$ can be expressed as $\text{e}\left( 1+px+q{{x}^{3}}+… \right)$ where $p$ and $q$ are constants to be determined.
[6]
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