Chapter 12.3, Problem 100AYU

To determine

To find: The sum of the first series is 6 and the sum of the second series.

Answer to Problem 100AYU

The sum of the first series is 6 and the sum of the second series is not possible.

Explanation of Solution

Given information:

Let us assume a geometric series that has first term, a = 2 and common ratio, r = $\frac{2}{3}$ and another geometric series that has first term, a = 2 and common ratio, r = $\frac{3}{2}$

Calculation:

Calculate the value of $S_{\infty }$ .

Use formula: $\begin{array}{c}{S}_{\infty }=\frac{a}{1-r}\\ =\frac{2}{1-\frac{2}{3}}\\ =6\end{array}$

Calculate the value of $S_{\infty }^{/}$ .

As the second series is divergent, it does not have a sum.

Therefore, the sum of the first series is 6 and the sum of the second series is not possible.