Chapter EP, Problem 11.4.13EP

To determine

To calculate: the sum of the given infinite geometric series.

Answer to Problem 11.4.13EP

  $Sum=\frac{2}{3}$

Explanation of Solution

The series can be expanded as $0.4,0.16,0.064,\mathrm{.......}$

In the given question, the sum of infinite geometric series needs to be calculated. The first term a is $0.4$ and the common ratio r is $0.4$ . Therefore, the sum can be calculated by using following formula:

  $Sum=\frac{a}{1-r}$

  $\begin{array}{l}Sum=\frac{0.4}{1-\left(0.4\right)}\\ Sum=\frac{0.4}{0.6}\\ Sum=\frac{4}{6}\\ Sum=\frac{2}{3}\end{array}$