Sequence of partial sum for the series is
(.) Behaviour of a series totally depends on the behaviour of the sequence of its partial sums i.e. if ,
(i) The series is said to be convergent if the sequence of partial sums is convergent . If the sequence converges to a real number , then is called sum of the series and we write
(ii) The series is said to be divergent if the sequence is divergent .
(.) Convergent sequence has a unique limit .