The sequence is .

A sequence is monotonic if it is either increasing or decreasing.

Check whether the sequence is increasing or decreasing.

 for all .

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For .

.

.

.

.

For .

.

.

.

Since , the sequence is increasing.

The sequence is : .

The sequence is bounded if , where is any finite number.

.

Therefore, the sequence is not bounded.

The sequence is increasing but not bounded.

The sequence is increasing but not bounded.