(a)

Convergent sequence:

A convergent sequence is a sequence whose limit is finite.

, where is a finite number.

Example 1:

The sequence is .

, is a finite number.

Therefore, the sequence is convergent.

Example 2:

The sequence is .

is a finite number.

Therefore, the sequence is convergent.

(b)

Divergent sequence:

A Divergent sequence is a sequence whose limit is either infinite or does not exist.

is or does not exist.

Example 1:

The sequence is .

.

Therefore, the sequence is a convergent sequence.

Example 2:

The sequence is .

is does not exist.

Therefore, the sequence is a convergent sequence.

(a) Convergent sequence: A convergent sequence is a sequence whose limit is finite.

, where is a finite number.

(b) Divergent sequence: A Divergent sequence is a sequence whose limit is either infinite or does not exist.

is or does not exist.