Chapter 12.3, Problem 89AYU

To determine

To find: The sum of infinite geometric series or multiplier.

Answer to Problem 89AYU

The multiplier is $10$ .

Explanation of Solution

Given information:

The given common difference of the series is $r=0.9$ .

Calculation:

Calculate the infinite series.

  ${\displaystyle \sum _{k=1}^{\infty }{a}_1{r}^{k-1}=\frac{a_1}{1-r}}$

Substitute the $1$ for $a_1$ and $0.9$ for $r$ .

  $\begin{array}{c}{\displaystyle \sum _{k=1}^{\infty }{a}_1{\left(0.9\right)}^{k-1}=\frac{1}{1-0.9}}\\ =\frac{1}{0.1}\\ \text{ =}10\end{array}$

Therefore, the multiplier is $10$ .