Binomial series for any rational powerEdexcel International A Level Maths: Mind map

Exam questions on Binomial series for any rational power

1. The function $f(x)=(1+4x)^{-\frac12}$ is expanded as a series in ascending powers of $x$.
   Find the term in $x^3$ in the expansion of $f(x)$.2 marks
2. The function $g(x)=\frac{1}{(2+x)^2}$ is expanded as a series in ascending powers of $x$.
   Use the expansion of $g(x)$ up to and including the term in $x^2$, with $x=0.1$, to estimate $\frac{1}{2.1^2}$ to 4 decimal places.2 marks
3. The function $h(x)=\sqrt[3]{8+3x}$ is expanded as a series in ascending powers of $x$.
   Find the expansion of $h(x)$ in ascending powers of $x$ up to and including the term in $x^2$, giving each coefficient as a fraction in its simplest form.3 marks