Chapter 12 - Sequences and Series - 12.4 Infinite Series - 12.4 Exercises - Page 639: 31

200

The total distance swing by the bob is $a_{1}+a_{2}+a_{3}+...=40+\frac{80\times40}{100}+\frac{80^{2}(40)}{100}+\frac{80^{3}(40)}{100}+..$ $=40[1+(\frac{80}{100})+(\frac{80}{100})^{2}+...]$ $=40(\frac{1}{1-\frac{4}{5}})=200$