A-Level CAIE Mathematics A2 1.6 Series Question Bank

Find the first three terms when $(2+3 x)^{6}$ is expanded in ascending powers of x.

In the expansion of $(1+a x)(2+3 x)^{6}$, the coefficient of $x^{2}$ is zero. Find the value of a.

Expand $(1+y)^{6}$ in ascending powers of y as far as the term in $y^{2}$.

In the expansion of $\left(1+\left(p x-2 x^{2}\right)\right)^{6}$ the coefficient of $x^{2}$ is 48 . Find the value of the positive constant p.

Find the coefficient of $x^{2}$ in the expansion of $\left(x-\frac{2}{x}\right)^{6}$.

Find the coefficient of $x^{2}$ in the expansion of $\left(2+3 x^{2}\right)\left(x-\frac{2}{x}\right)^{6}$.

Find the first 3 terms in the expansion of $(2-y)^{5}$ in ascending powers of y.

Use the result in part (i) to find the coefficient of $x^{2}$ in the expansion of $\left(2-\left(2 x-x^{2}\right)\right)^{5}$.

Expand $\left(1-\frac{1}{2 x}\right)^{2}$.

Find the first four terms in the expansion, in ascending powers of x, of $(1+2 x)^{6}$.

Hence find the coefficient of x in the expansion of $\left(1-\frac{1}{2 x}\right)^{2}(1+2 x)^{6}$.