Chapter 8.1, Problem 14E

To determine

To write: the first five terms of the sequence.

Answer to Problem 14E

The first five terms of the sequence are $\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},$ and $\frac{5}{6}$ .

Explanation of Solution

Given information:

Given sequence

  $a_n=\frac{n}{n+1}$

Calculation:

Substitute 1 for $n$ is $a_n=\frac{n}{n+1}$ .

  $\begin{array}{c}{a}_1=\frac{1}{1+1}\\ =\frac{1}{2}\end{array}$

Thus, the first term of the sequence is $\frac{1}{2}$

Similarly, substitute 2,3,4,and 5 for $n$ is $a_n=\frac{n}{n+1}$ .

The second term is $\frac{2}{3}$ , the third term is $\frac{3}{4}$ , the fourth term is $\frac{4}{5}$ , and the fifth term is $\frac{5}{6}$ .

Therefore, the first five terms of the sequence are $\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},$ and $\frac{5}{6}$ .

The table feature of the graphing utility gives the same terms as the first five terms of the sequence. Thus, the result is verified.