Why do mathematicians like to shift things around all the time when they write stuff?

For example the arithmetic series was on the far right, then in the next step he puts it in them middle of the equation.

I see this all the time in every text book, they always move bits around.

Isn't it more logical to keep things the same? Why isn't it $na\Delta x+(\Delta x^{2})(\frac{n(n+1)}{2})$?