Chapter 8.4, Problem 17E

To determine

Find the total distance swings by the cousin.

Answer to Problem 17E

Thetotal distances swings by the cousin are $56$ feet.

Explanation of Solution

Given:

The cousin swings the distances are shown in the figure

  

Calculation:

The figure shows the geometric series.

  $14+14\left(0.75\right)+14{\left(0.75\right)}^2+\cdot \cdot \cdot$

The sum of an infinite geometric series with first term $a_1$ and common ratio $r$ is

  $S=\frac{a_1}{1-r}$ , where $r<1$ .

If $r\ge 1$ , then the series has no sum.

In the given series $a_1=14$ and $r=0.75<1$ .

  $\begin{array}{l}S=\frac{14}{1-0.75}\\ =\frac{14}{\frac{0.25}{3}}\\ =56\end{array}$

Hence the total distances swings by thecousin are $56$ feet.