Chapter 12.3, Problem 3CFU

To determine

To explain:

The example of infinity geometric series having the sum.

Answer to Problem 3CFU

The example of infinity geometric series is $27+18+12+\mathrm{8....}$ and this series does not have the sum.

Explanation of Solution

In order to calculate the sum of an infinite geometric series, the common ratio $r$ must be between $-1$ and $1$ .

If any geometric series have the common ratio greater than $1$ , then that series does not posse’s sum.

The geometrical sum of series is $S=\frac{a_1}{1-r}$ .

As an example:

The following series $27+18+12+\mathrm{8....}$ has the common ratio of $\frac{3}{2}>1$ . Thus, this series does not have the sum.