The first term of the sequence is .

The term of the sequence is .

(a)

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

Check whether the sequence is increasing or decreasing.

 for all .

For .

.

.

.

.

For .

.

.

.

.

Since , the sequence is increasing.

Therefore, the sequence is monotonic sequence.

The sequence is : .

Consider .

.

.

Therefore, .

Therefore, the sequence is bounded by .

Since the sequence is bounded and monotonic, it is convergent.

Hence, is exists.

(b)

The term of the sequence is .

or

or .

Since the sequence is increasing, .

(a) The sequence is increasing and bounded by .

is exists.

(b) The limit of the sequence is .