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Assume that the nth term in the sequence of partial sums for the series no an is given below. Determine if the series no...

Assume that the nth term in the sequence of partial sums for the series no an is given below. Determine if the series no an is convergent or divergent. If the series is convergent determine the value of the series. 5+8n² Sn 2-7n² =
Transcribed: Assume that the nth term in the sequence of partial sums for the series Σn=0 an is given below. -o an is convergent or divergent. If the series is convergent determine the Determine if the series value of the series. 5+8n² Sn 2-7n² =

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

(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 .

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