Chapter 11.6, Problem 5OE

To determine

To calculate:

Common ratio of given geometric series and sum series has.

Answer to Problem 5OE

Common ratio of given geometric series is $1.73$ and a sum is $-1.36$ .

Explanation of Solution

Give information:

  $1+\sqrt{3}+3+\mathrm{...}$

Calculation:

In order to find out common ratio of given number,

  $1+\sqrt{3}+3$

Common ratio $\left(r\right)$ is calculated as,

  $\begin{array}{l}=\frac{t_2}{t_1}\\ =\frac{\sqrt{3}}{1}\\ =1.73\end{array}$

Or

  $\begin{array}{l}=\frac{3}{\sqrt{3}}\\ =1.73\end{array}$

Sum of given geometric series is calculated as,

  $S=\frac{a_1}{1-r}$

Where,

  $a_1=$ Initial term.

Put the values in the equation.

  $\begin{array}{l}S=\frac{1}{1-\left(1.73\right)}\\ S=-1.36\end{array}$

Therefore, Common ratio of given geometric series is $1.73$ and a sum is $-1.36$ .