Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 815: 56a

$\dfrac{x^{5}-1}{x-1}$

Here, we have a common ratio $r=x$ and $a_1= 1$ We are given that $S_5= (1) \sum_{i=1}^5 x^{i-1}$ We know that $S_{n}=a_1(\dfrac{r^{n}-1}{r-1})$ Common ratio $r=x$ and $a_1= 1$ Plug in $n=5$ Hence, $S_{5}=\dfrac{x^{5}-1}{x-1}$