(a)

Find the sequence is convergent or divergent.

The sequence is where .

The first term is .

Write out the terms of the sequence.

Terms of the sequence :

.

.

.

Observe the values :

The sequence is oscillates in between the values .

Therefore, the sequence is divergent.

(b)

What happens when the first term is .

Write out the terms of the sequence.

Terms of the sequence :

.

.

.

observe the values.

The sequence is convergent at .

(a). The sequence is divergent for the first term is .

(b). The sequence is convergent for the first term is .