WeBWorK Standalone Renderer

Consider the sequence $\displaystyle{\lbrace a_n \rbrace = \left\lbrace {\frac{3n+1}{3n}-\frac{3n}{3n+1}} \right\rbrace }$ . Graph this sequence and use your graph to help you answer the following questions.

Part 1: Is the sequence bounded?

Is the sequence $\lbrace a_n \rbrace$ bounded above by a number? If yes, what number? Enter a number or enter DNE.

Is the sequence $\lbrace a_n \rbrace$ bounded below by a number? If yes, what number? Enter a number or enter DNE.

Select all that apply: The sequence $\lbrace a_n \rbrace$ is
A. bounded below.
B. bounded above.
C. unbounded.
D. bounded.

Part 2: Is the sequence monotonic?

The sequence $\lbrace a_n \rbrace$ is

A. alternating
B. decreasing.
C. increasing.
D. none of the above

Part 3: Does the sequence converge?

The sequence $\lbrace a_n \rbrace$ is .

The limit of the sequence $\lbrace a_n \rbrace$ is . Enter a number or DNE.

You can earn partial credit on this problem.