Find the sum of the series as a function of x.
-$$\sum _ { n = 1 } ^ { \infty } ( x - 8 ) ^ { n }$$
A) $- \frac { x - 8 } { x - 7 }$
B) $\frac { x - 8 } { x - 9 }$
C) $- \frac { x - 8 } { x - 9 }$
D) $\frac { x - 8 } { x - 7 }$

Question

Quizplus · Accepted Answer

The given series is a geometric series with first term $a=x-8$ and common ratio $r=x-8$. Thus, the sum of the series is:
\begin{align*}
\frac{a}{1-r}&=\frac{x-8}{1-(x-8)}=-\frac{x-8}{x-9}
\end{align*}
Therefore, the correct choice is (C).

Find the Sum of the Series as a Function of X