On first look, doesn't any number suffice? For example, if I let $n=1$ then $1+\frac{1}{10} < \alpha < 1+\frac{2}{10}$ is valid right? Tho, I think the question is asking in the context of the rest of the question? Am at part iv
I don't really get the reasoning behind the answer tho
How does the pieces fall into place? Why the expression for $g(x)$. How do I get the seemingly arbitrary numbers 1.7 and 1.8?