Moderate -0.3 This is a straightforward binomial expansion question requiring recall of the general binomial theorem formula and substitution. While it involves negative/fractional powers and finding the validity range, these are standard C2/C4 techniques. The approximation part is mechanical substitution rather than requiring insight. Slightly easier than average due to being mostly procedural with clear steps.
Write down the first three terms in the binomial expansion of \((1-4x)^{-\frac{1}{2}}\) in ascending powers of \(x\). State the range of values of \(x\) for which the expansion is valid. By writing \(x = \frac{1}{13}\) in your expansion, find an approximate value for \(\sqrt{13}\) in the form \(\frac{a}{b}\), where \(a\), \(b\) are integers. [5]
Write down the first three terms in the binomial expansion of $(1-4x)^{-\frac{1}{2}}$ in ascending powers of $x$. State the range of values of $x$ for which the expansion is valid. By writing $x = \frac{1}{13}$ in your expansion, find an approximate value for $\sqrt{13}$ in the form $\frac{a}{b}$, where $a$, $b$ are integers. [5]
\hfill \mbox{\textit{WJEC Unit 3 2018 Q6 [5]}}