Chapter 8.3, Problem 4E

(a) The nth partial sum of a geometric sequence $a_n=a{r}^{n-1}$ is given by $Sn=\_\_\_\_\_\_.$
(b) The series ${\displaystyle \underset{k=1}{\overset{\infty }{\sum }}a{r}^{k-1}}=a+ar+a{r}^2+a{r}^3+\mathrm{......}$ is an infinite _________, series. If $\left|r\right|\ge 1,$ then this series _________, and its sum is $S=\_\_\_\_\_\_\_.$ If $\left|r\right|\ge 1,$ the series _________.