Consider the sequence $\displaystyle{\lbrace a_n \rbrace = \left\lbrace {\frac{\left(-1\right)^{n}\cdot 9n}{n+1}} \right\rbrace }$. Graph this sequence and use your graph to help you answer the following questions.

1. Is the sequence $\lbrace a_n \rbrace$ bounded above by a function? If it is, enter the function of the variable $n$ that provides the “best” and “most obvious” upper bound; otherwise, enter DNE for does not exist.
2. What is the limit of the function from part (a) as $n \to \infty$? Enter a number, or enter DNE.
3. Is the sequence $\lbrace a_n \rbrace$ bounded below by a function? If it is, enter the function of the variable $n$ that provides the “best” and “most obvious” lower bound; otherwise, enter DNE for does not exist.
4. What is the limit of the function from part (c) as $n \to \infty$? Enter a number, or enter DNE.
5. Is the sequence $\lbrace a_n \rbrace$ bounded above by a number? Enter a number or enter DNE.
6. Is the sequence $\lbrace a_n \rbrace$ bounded below by a number? Enter a number or enter DNE.
7. Select all that apply: The sequence $\lbrace a_n \rbrace$ is

The sequence $\lbrace a_n \rbrace$ is

1. The sequence $\lbrace a_n \rbrace$ is .
2. The limit of the sequence $\lbrace a_n \rbrace$ is . Enter a number or DNE.
1. When you first look at the sequence $\displaystyle \left\lbrace \frac{\left(-1\right)^{n}\cdot 9n}{n+1} \right\rbrace$, you expect it to

2. When you first look at the sequence $\displaystyle \left\lbrace \frac{\left(-1\right)^{n}\cdot 9}{n+1} \right\rbrace$, you expect it to

3. If a sequence is alternating, it converge.