mattgondek4
2020-11-23
Answered

Determine if the series $\sum _{n=0}^{\mathrm{\infty}}{a}_{n}$ is convergent or divergent if the partial sum of the n terms of the series is given below. If the series is convergent, determine the value of the series.

$S}_{n}=\frac{5+8{n}^{2}}{2-7{n}^{2}$

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krolaniaN

Answered 2020-11-24
Author has **86** answers

Result on convergence of series:

If the sequence of partial sum

Moreover, the sum of the series is given by

Now, the given sequence of partial sum is

Writing the first few terms of the sequence,

Clearly, the sequence is monotonically increasing.

Also it is bounded above by'0' that is

Hence, the given sequence of partial sum is convergent.

In order to get the sum of the series, we will find the limit of the given sequence of partial sum.

Hence,

Jeffrey Jordon

Answered 2022-01-14
Author has **2262** answers

Answer is given below (on video)

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