Chapter 8.1, Problem 1E

(a)

To determine

To Find: The definition of the sequence.

Answer to Problem 1E

The term sequence is defined.

Explanation of Solution

Calculation:

Consider that the sequence is defined by ordered list of number as,

  $\left\{a_1,a_2,a_3,a_4\mathrm{.......}{a}_n\right\}$

Thus, the sequence is then defined as the function with positive domain as the set of positive integer.

(b)

To determine

To Find: The meaning for the $\underset{n\to \infty }{\lim }{a}_n=8$ .

Answer to Problem 1E

As the term $a_n$ approaches infinity the value is 8.

Explanation of Solution

Calculation:

Consider the given term $\underset{n\to \infty }{\lim }{a}_n=8$ .

The above function shows that as the term $a_n$ approaches infinity the value is 8.

(c)

To determine

To Find: The meaning for the $\underset{n\to \infty }{\lim }{a}_n=\infty$ .

Answer to Problem 1E

The term $\underset{n\to \infty }{\lim }{a}_n=\infty$ means that as the nth term approaches infinity the value of the term approaches to infinity.

Explanation of Solution

Calculation:

Consider the term $\underset{n\to \infty }{\lim }{a}_n=\infty$ .

The term $\underset{n\to \infty }{\lim }{a}_n=\infty$ means that as the nth term approaches infinity the value of the term approaches to infinity.