Mathematics 9709 · AS & A Level · Algebra
Expand $\frac{1}{\sqrt{1 - 4x}}$ as a series in ascending powers of $x$, including terms up to and including $x^2$, and simplify the coefficients.
Hence find the coefficient of $x^2$ that appears in the expansion of $\frac{1 + 2x}{\sqrt{4 - 16x}}$.
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find the correct, unsimplified $x$ term or $x^2$ term from $\sqrt{1-4x}$, or else differentiate and evaluate $f(0)$ and $f'(0)$ where $f(x)=k\sqrt{1-4x}$” …