Sequence of partial sum for the series $\sum _{n=}^{\infty}{a}_{n}$ is ${S}_{n}=\frac{5+8{n}^{2}}{2-7{n}^{2}}$
(.) Behaviour of a series $\sum _{n=1}^{\infty}{a}_{n}$ totally depends on the behaviour of the sequence of its partial sums $<{S}_{n}>$ i.e. if ,
(i) The series $\sum _{n=1}^{\infty}{a}_{n}$ is said to be convergent if the sequence of partial sums $<{S}_{n}>$ is convergent . If the sequence $<{S}_{n}>$ converges to a real number $S$ , then $S$ is called sum of the series and we write $\sum _{n=1}^{\infty}{a}_{n}=S$
(ii) The series $\sum _{n=1}^{\infty}{a}_{n}$ is said to be divergent if the sequence$<{S}_{n}>$ is divergent .
(.) Convergent sequence has a unique limit .