Chapter 8.1, Problem 24E

(a)

To determine

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

Answer to Problem 24E

Five terms of this sequence are $-\frac{1}{2},\frac{2}{3},-\frac{3}{4},\frac{4}{5},-\frac{5}{6}$ respectively.

Explanation of Solution

Given information:

Given sequence

  $a_n={\left(-1\right)}^n\left(\frac{n}{n+1}\right)$

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 24E

Five terms of this sequence are $-\frac{1}{2},\frac{2}{3},-\frac{3}{4},\frac{4}{5},-\frac{5}{6}$ respectively.

Explanation of Solution

Calculation:

Given sequence

  $a_n={\left(-1\right)}^n\left(\frac{n}{n+1}\right)$

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

  $\begin{array}{c}{a}_1={\left(-1\right)}^1\left(\frac{1}{1+1}\right)\\ =-\frac{1}{2}\\ =-0.5\\ a_2={\left(-1\right)}^2\left(\frac{2}{2+1}\right)\\ =\frac{2}{3}\\ =0.66667\\ a_3={\left(-1\right)}^3\left(\frac{3}{3+1}\right)\\ =-\frac{3}{4}\\ =-0.75\\ a_4={\left(-1\right)}^4\left(\frac{4}{4+1}\right)\\ =\frac{4}{5}\\ =0.8\\ a_5={\left(-1\right)}^5\left(\frac{5}{5+1}\right)\\ =-\frac{5}{6}\\ =-0.8333\end{array}$

Hence, five terms of this sequence are $-\frac{1}{2},\frac{2}{3},-\frac{3}{4},\frac{4}{5},-\frac{5}{6}$ respectively. So, it is clear that values obtained from both methods, are same.