Here are short justification of changes I'm proposing.
The first change is there because of a missing word in that sentence.
If we use sum of geometric series on \frac{1}{q^n} + \frac{1}{q^{n-1}} + \cdots + \frac{1}{q} we get \frac{1}{q-1}\inparen{1-\frac{1}{q^n}} and hence justifies the correction.
Here are short justification of changes I'm proposing.