Question

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

Answer 1

Step 1:

The sequence .

A sequence is monotonic if it is either incresing or decresing.

Check whether the sequence is incresing or decresing.

for all .

For .

For .

Since for all , the sequence is decreasing.

Step 2:

The sequence is :

The sequence is bounded if .

Therefore, the sequence is bounded.

Solution:

The sequence is decreasing and bounded.