Chapter 11.6, Problem 27WE

To determine

To explain:

No infinite geometric series with first term $10$ and sum $4$ .

Answer to Problem 27WE

As $\left|r\right|=1.5=1.5>1$ , there is no infinite geometric series where $t_1=10,S=4$

Explanation of Solution

The formula for h sum of $n$ terms is given by $S=\frac{t_1}{1-r}$

Given is $r=\frac{2}{5},S=125$ ,

Use the formula of the sum of an infinite geometric series,

  $S=\frac{t_1}{1-r}$

It is given that $S$ is $4$ and $t_1$ is $10$ , so need to solve for $r$ ,

  $\begin{array}{l}S=\frac{t_1}{1-r}\\ 4=\frac{10}{1-r}\\ r=-1.5\end{array}$

  $\left|r\right|=1.5$

  $1.5>1$

Th condition for existence of sum of an infinite series is given by $-1<r<1$

But here $\left|r\right|=1.5$ which is greater than $1$

Therefore, there is no infinite geometric series where $t_1=10,S=4$