Question

Determine whether the sequence with the given nth term is monotonic and whether it is bounded. use a graphing utility to confirm your results.

Answer 1

Step 1:

The sequence is .

The first term is .

The second term is .

The third term is .

The forth term is

The sequence is .

 A sequence is monotonic if its terms are non increasing .

The terms in the sequence

Therefore, the sequence is monotonic.

Step 2:

The sequence is .

The terms in the sequence are .

The sequence is between  to .

The upper bound of the sequence is .

.

The lower bound of the sequence is .

.

The sequence is bounded between .

The sequence is bounded.

Step 3:

Graph the sequence .

Observe the graph:

The sequence is bounded between to .

Solution:

The sequence is monotonic and bounded.