Chapter SH, Problem 10.13EP

To determine

To find: The sum of the given infinite series if it exists.

Answer to Problem 10.13EP

There is no sum exists

Explanation of Solution

Given:

The given sequence is $-5+\left(-12\right)+\left(-28.8\right)+\mathrm{...}$ .

Calculation:

The formula for the sum of an infinite geometric series with $-1<r<1$ is given by $S=\frac{a_1}{1-r}$ .

Sun will exist if the common ratio is between $-1<r<1$ .

Find the common ratio as follows.

  $\begin{array}{c}\frac{-12}{-5}=2.4\\ \frac{-28.8}{-12}=2.4\\ ⋮\end{array}$

The ratio is $2.4$ , whose absolute value is not less than 1. So, sum will not exist.

Therefore, there is no sum exists.