Expand $\frac{\sqrt{4+x}}{1-x}$ in ascending powers of $x$, up to and including the term in \({{

Question

Expand $\frac{\sqrt{4+x}}{1-x}$ in ascending powers of $x$, up to and including the term in ${{x}^{2}}$. State the set of values of x for which the expansion is valid.[5] By substituting $x=-\frac{1}{10}$, obtain an estimate for $\sqrt{390}$, leaving your answer as a fraction.[2]

Accepted Answer

(i) $2+\frac{9}{4}x+\frac{143}{64}{{x}^{2}}+\cdots $$\left\{ x\in \mathbb{R}:\ -1<x<1 \right\}$ (ii) $\sqrt{390}\approx \frac{126533}{6400}$

2013 YJC P1 Q8

2013 YJC P1 Q8

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