3.78: Binomial expansions of $(1 + 7x)^{5}$ and $(2 - kx)^{8}$

Find the first three terms in the expansion of $\left(1 + \dfrac{x}{7}\right)^{5}$, in ascending powers of $x$. Simplify the coefficient of each term.

The expansion of $(7 + nx)\left(1 + \dfrac{x}{7}\right)^{5}$, where $n$ is a positive integer, is written in ascending powers of $x$. The first two terms in the expansion are $7 + 89x$. Find the value of $n$.

In the expansion of $(k - 2x)^{8}$, where $k$ is a constant, the coefficient of $x^{4}$ divided by the coefficient of $x^{2}$ is $\dfrac{5}{8}$. The coefficient of $x$ is positive. Form an equation and hence find the value of $k$.