Chapter 11.6, Problem 2P

To determine

To calculate:

Man end up his walk for given condition.

Answer to Problem 2P

Man end up his walk at $\frac{2}{3}$ mi east.

Explanation of Solution

Give information:

  $1$ mi east,

  $\frac{1}{2}$ mi west,

  $\frac{1}{4}$ mi east,

  $\frac{1}{8}$ mi west.

Calculation:

Given values are,

  $1,\frac{1}{2},\frac{1}{4},\frac{1}{8}$

So this is a geometric series with ratio of $-1/2$ ,

  $\begin{array}{l}{\displaystyle {\sum }_{k=0}^{\infty }{\left(-\frac{1}{2}\right)}^k}\\ =\frac{1}{1+1/2}\\ =\frac{2}{3}\end{array}$

Therefore, Man end up his walk at $\frac{2}{3}$ mi east.