(a)(i) Find the first three terms in the expansion of

\(\left(1+\frac{x}{7}\right)^5\)

in ascending powers of \(x\). Simplify the coefficient of each term.

(a)(ii) The expansion of

\(7(1+x)^n\left(1+\frac{x}{7}\right)^5,\)

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 \(n\).

(b) 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 \(\frac58\). The coefficient of \(x\) is positive. Form an equation and hence find the value of \(k\).