Chapter 8.4, Problem 29E

To determine

To show that both series have finite sums and also find whether the person catch up the tortoise.

Answer to Problem 29E

Yes.

Explanation of Solution

Given:

The given table is

Calculation:

Using the sum of infinite terms of GP to calculate the distance and time sums as follows-

The total distance is −

  $\begin{array}{l}{\displaystyle {\sum }_{n=1}^{\infty }20{(0.5)}^{n-1}}\\ S=\frac{a_1}{1-r}=\frac{20}{1-\frac{1}{2}}=\frac{20}{\frac{1}{2}}=40\end{array}$

The total time is −

  $\begin{array}{l}{\displaystyle {\sum }_{n=1}^{\infty }1{(0.5)}^{n-1}}\\ S=\frac{a_1}{1-r}=\frac{1}{1-\frac{1}{2}}=\frac{1}{\frac{1}{2}}=2\end{array}$

Hence it is proved that both are finite sums and person will be able to catch the tortoise.