2.12: Binomial expansion with negative powers

Given that $\left(x^{2} - \tfrac{1}{px}\right)^{8} = x^{16} - 4x^{13} + qx^{10} + rx^{7} + \dots$, find the value of each of the constants $p$, $q$ and $r$.

Explain why there is no term independent of $x$ in the binomial expansion of $\left(x^{2} - \tfrac{1}{px}\right)^{8}$.

In the binomial expansion of $\left(1 - \tfrac{\sqrt{x}}{2}\right)^{n}$, where $n$ is a positive integer, the coefficient of $x$ is 30. Form an equation in $n$ and hence find the value of $n$.