Question 4.16 had a mistake that has now been corrected.

For 4.29 a useful trick is to multiply the whole series by $r$, that is, if you have the sum with $n$ terms $S_n = \displaystyle \sum_{k=0} ^{n-1} a_0\cdot r^k = a+ar+ar^2+\cdots+ar^{n-1} $, $r$ times that sum is equal to $r\cdot S_n = ar + ar^2 + ar^3 + \cdots + ar^n$. Note that these two ($S_n$ and $r\cdot S_n$) have a lot of terms in common. You can use this two expressions to solve for the sum $S_n$.