Chapter 11.6, Problem 1WE

To determine

To calculate:

Sum of given geometric series.

Answer to Problem 1WE

Sum of given geometric series is $\frac{24}{1}$ .

Explanation of Solution

Give information:

  $24+12+6+3+\mathrm{...}$

Calculation:

In order to find out common ratio of given number,

  $24+12+6+3$

Here first term is $a_1=24$

So common ratio is $r=\frac{12}{24}=\frac{1}{2}$

Since $\left|r\right|=\left|\frac{1}{2}\right|<1$

Infinite sum exists.

So, Sum of given geometric series is calculated as,

  $=\frac{a^n}{1-r}$

Where,

  $a_1=$ Initial term.

  $r=$ common ratio between terms.

  $n=$ number of terms

Put the values in the equation.

  $\begin{array}{l}=\frac{a^n}{1-r}\\ =\frac{24}{1-\left(\frac{1}{2}\right)}\\ =\frac{24}{1}\end{array}$

Therefore, sum of given geometric series is $\frac{24}{1}$ .