Chapter 11.4, Problem 69E

To determine

To find: Whether the sequence converges or diverges and if the sequence converges find the limit.

Answer to Problem 69E

The given sequence diverges.

Explanation of Solution

Given Data:

The given sequence is,

  ${\mathrm{a}}_{\mathrm{n}}=\frac{3\left[1-{\left(1.5\right)}^{\mathrm{n}}\right]}{1-1.5}$

Calculation:

Consider the sequence is,

  ${\mathrm{a}}_{\mathrm{n}}=\frac{3\left[1-{\left(1.5\right)}^{\mathrm{n}}\right]}{1-1.5}$

In the graphing calculator select the mode as shown in Figure 1

  

Figure 1

Input the sequence as shown in Figure 2

  

Figure 2

Adjust the viewing window as shown in Figure 3

  

Figure 3

Press the graph button as shown in Figure 4

  

Figure 4

The above figure shows that the sequence diverges.