Chapter 11.6, Problem 48STP

To determine

The sum of each infinite geometric series

Answer to Problem 48STP

The sum is $\frac{\sqrt{3}}{\left(1-\sqrt{3}\right)}$ .

Explanation of Solution

Given information:

Geometric Series $\sqrt{3}+3+\sqrt{27}+\mathrm{...}$

Concept Used:

The Sum of Geometric series is given by the formula

  $sum=\frac{a}{\left(1-r\right)}$

Calculation:

In order to find the sum and the common ratio between two number r and simplify further as shown below,

  $\begin{array}{c}\text{Common ratio}\\ r=\frac{a_2}{a_1}\\ r=\frac{3}{\sqrt{3}}=\sqrt{3}\\ \text{Sum}\\ sum=\frac{a}{\left(1-r\right)}\\ =\frac{\sqrt{3}}{\left(1-\sqrt{3}\right)}\end{array}$

Thus, the sum is $\frac{\sqrt{3}}{\left(1-\sqrt{3}\right)}$ .