Chapter 8.1, Problem 19E

(a)

To determine

To write the first five terms of the given sequence using table feature of a graphing utility.

Answer to Problem 19E

Five terms of this sequence are $0.5,0.75,0.875,0.9375,0.96875$ respectively.

Explanation of Solution

Given information:

Given sequence

  $a_n=1-\frac{1}{2^n}$

Calculation:

To have the first five terms by graphical utility, firstly click on $Y=$ button of Ti-83 calculator and then write down the provided function of the problem, as shown below:

  

Now, Set the table setup. For this, click on $2^{nd}$ and then click on WINDOW button. After this a new screen appears, In this, set the indpnt as Ask. The screenshot is given below:

  

After this, click on $2^{nd}$ and then click on GRAPH button. After this, a new screen appears. In this, input the degrees to have the required table. The screenshot is given as below:

  

(b)

To determine

To write the first five terms of the given sequence algebraically.

Answer to Problem 19E

Five terms of this sequence are $0.5,0.75,0.875,0.9375,0.96875$ respectively.

Explanation of Solution

Calculation:

Value of $n$ begins with1, for five terms of this sequence put $n=1,2,3,4,5$ . So,

  $\begin{array}{c}{a}_1=1-\frac{1}{2^1}\\ =\frac{1}{2}\\ =0.5\\ a_2=1-\frac{1}{2^2}\\ =\frac{3}{4}\\ =0.75\\ a_3=1-\frac{1}{2^3}\\ =\frac{7}{8}\\ =0.875\\ a_4=1-\frac{1}{2^4}\\ =\frac{15}{16}\\ =0.9375\\ a_5=1-\frac{1}{2^5}\\ =\frac{31}{32}\\ =0.96875\end{array}$

Hence, five terms of this sequence are $0.5,0.75,0.875,0.9375,0.96875$ respectively. So, it is clear that values obtained from both methods, are same.