Chapter EP, Problem 11.4.10EP

To determine

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

Answer to Problem 11.4.10EP

  $Sum=4$

Explanation of Solution

The series can be expanded as $3,\frac{3}{4},\frac{3}{16},\frac{3}{64}\mathrm{.......}$

In the given question, the sum of infinite geometric series needs to be calculated. The first term a is $3$ and the common ratio r is $\frac{1}{4}$ . Therefore, the sum can be calculated by using following formula:

  $Sum=\frac{a}{1-r}$

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