Series

Find the complete expansion of $\left(2x - \frac{3}{x}\right)^4$.

Hence determine the coefficient of $x^2$ in the expansion of $(x^2 + 5)\left(2x - \frac{3}{x}\right)^4$.

Find the common ratio.

The first nine terms of the progression are now removed.

Find the sum to infinity of the remaining terms of the progression.

Find the tenth term of the progression. Give your answer correct to 3 significant figures.

Find the exact value of the sum to infinity of the progression.

$(2 - px)^5$

$\left(1 - \frac{1}{2}x\right)^4$

Given that the coefficient of $x^2$ in the expansion of $(2 - px)^5 \left(1 - \frac{1}{2}x\right)^4$ is 93, find the possible values of the constant $p$.

Find the value of $k$.

Find the sum of the first 20 terms of the progression.

The fourth and sixth terms of a geometric progression are 36 and 6 respectively. The common ratio of the progression is positive.

Find the sum to infinity of the progression. Give your answer in the form $\frac{a}{\sqrt{b}-c}$, where $a$, $b$ and $c$ are integers.

Find the first three terms in the expansion of $\left( 2 - \frac{3}{2}x \right)^5$ in ascending powers of $x$.

Use your answer to part (a), with a suitable value of $x$, to find an approximation to $1.985^5$.